Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze40.0ms (0.3%)

Memory

35.2MiB live, 72.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.9s (44%)

Memory

77.1MiB live, 8 305.3MiB allocated

Samples

3.4s	25 913×	0	invalid
674.0ms	5 524×	0	valid
593.0ms	2 732×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

const: 669.0ms (22.5% of total)

ival-tan: 640.0ms (21.5% of total)

ival-mult: 292.0ms (9.8% of total)

ival-add: 281.0ms (9.5% of total)

ival-<=: 271.0ms (9.1% of total)

ival-fabs: 247.0ms (8.3% of total)

ival-sub: 181.0ms (6.1% of total)

ival-<: 163.0ms (5.5% of total)

ival-and: 92.0ms (3.1% of total)

adjust: 84.0ms (2.8% of total)

exact: 39.0ms (1.3% of total)

ival-assert: 11.0ms (0.4% of total)

Bogosity

explain159.0ms (1%)

Memory

13.9MiB live, 109.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
228	2	(2.3706992799901014e-209 2.3665143017691485e-211)	4	(-2.3629683525822773e-98 3.7902516320372213e-100)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
2	0	-	1	(19.128802365450515 7.539848339383705e-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	226	9
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	225	4
-	2	25

Precision

0.9911894273127754

Recall

0.982532751091703

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	225	4	0
-	2	5	20

Precision?

0.9703389830508474

Recall?

1.0

Freqs

test

number	freq
0	29
1	227

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

67.0ms	344×	0	valid
16.0ms	168×	1	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-tan: 60.0ms (86.5% of total)

adjust: 4.0ms (5.8% of total)

ival-sub: 3.0ms (4.3% of total)

ival-add: 3.0ms (4.3% of total)

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

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

preprocess47.0ms (0.3%)

Memory

-15.9MiB live, 23.4MiB 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))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (0.3%)

Memory

-2.7MiB live, 36.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.0585384450664193	(tan.f64 (+.f64 x eps))
accuracy	23.230795081529713	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

28.0ms	172×	0	valid
9.0ms	84×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-tan: 24.0ms (83.9% of total)

adjust: 2.0ms (7% of total)

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

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

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

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

series33.0ms (0.2%)

Memory

-21.2MiB live, 17.9MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (/ (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
22.0ms	x	@	0	(tan x)
2.0ms	eps	@	0	(- (tan (+ x eps)) (tan x))
2.0ms	eps	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	0	(- (tan (+ x eps)) (tan x))

simplify336.0ms (2.1%)

Memory

12.6MiB live, 405.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1351
1	464	1285
2	1534	1274
3	5949	1242
0	8534	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite244.0ms (1.6%)

Memory

5.5MiB live, 386.5MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 259

Calls

Call 1

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

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

eval40.0ms (0.3%)

Memory: -9.8MiB live, 113.2MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune64.0ms (0.4%)

Memory

9.0MiB live, 208.7MiB allocated

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	315	21	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	315	22	337

Accuracy

100.0%

Counts

337 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	63.8%	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))))
	62.5%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (sin.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
▶	62.6%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	63.7%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	39.5%	(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
	63.7%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	24.6%	(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
	39.3%	(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
✓	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
▶	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
	62.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
	36.7%	(-.f64 (tan.f64 (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) (tan.f64 x))
	62.7%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 1 117 to 542 computations (51.5% saved)

simplify229.0ms (1.5%)

Memory

0.9MiB live, 435.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	512	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64)))
cost-diff	6720	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff	7040	(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff	7488	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
cost-diff	0	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
cost-diff	0	(fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))
cost-diff	0	(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))
cost-diff	0	(tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x)))))
cost-diff	0	(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
cost-diff	0	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
cost-diff	0	(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	192	(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64))
cost-diff	26816	(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))

Rules

13 546×	`lower-fma.f32`
13 528×	`lower-fma.f64`
4 124×	`lower-*.f32`
4 106×	`lower-*.f64`
2 094×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	855
0	120	828
1	222	742
2	512	729
3	1540	722
4	5753	722
0	8226	711

Stop Event

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

Calls

Call 1

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

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

localize296.0ms (1.9%)

Memory

-10.0MiB live, 424.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.265625	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
accuracy	0.320976269536884	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy	23.37091175018826	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64)))
accuracy	0.01953125	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.02734375	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.0390625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.8947363595148837	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
accuracy	0.1015625	(*.f64 eps (-.f64 eps x))
accuracy	0.1171875	(fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))
accuracy	23.230795081529713	(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
accuracy	39.44355161916248	(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))
accuracy	0.0585384450664193	(tan.f64 (+.f64 x eps))
accuracy	0.375	(*.f64 x #s(literal 1/3 binary64))
accuracy	1.1516378574382184	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
accuracy	23.230795081529713	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
accuracy	0.04982377930532605	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.125	(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.38721220768770737	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	0.963222509768442	(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64))

Samples

101.0ms	167×	0	valid
89.0ms	87×	1	valid
3.0ms	2×	2	valid

Compiler

Compiled 778 to 67 computations (91.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-mult: 33.0ms (21.5% of total)

ival-add: 32.0ms (20.8% of total)

ival-tan: 21.0ms (13.7% of total)

ival-div: 15.0ms (9.8% of total)

adjust: 13.0ms (8.5% of total)

ival-pow: 10.0ms (6.5% of total)

const: 9.0ms (5.9% of total)

ival-sub: 8.0ms (5.2% of total)

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

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

ival-cos: 2.0ms (1.3% of total)

exact: 1.0ms (0.7% of total)

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

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

series109.0ms (0.7%)

Memory

18.5MiB live, 127.2MiB allocated

Counts

26 → 528

Calls

Call 1

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

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/3 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (patch (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 4/3 (pow x 2))) (taylor 0 x) (#s(alt (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (patch (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) (taylor 0 x) (#s(alt (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (patch (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* eps (sin x)) (cos x)) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())

Calls

132 calls:

Time	Variable		Point	Expression
10.0ms	x	@	inf	(/ (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (* (- 1 (* (tan x) (tan eps))) (/ 1 (tan x))))
9.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
5.0ms	eps	@	0	(/ (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (* (- 1 (* (tan x) (tan eps))) (/ 1 (tan x))))
4.0ms	eps	@	inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
3.0ms	x	@	-inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)

simplify283.0ms (1.8%)

Memory

13.1MiB live, 376.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 960×	`lower-fma.f64`
9 960×	`lower-fma.f32`
6 546×	`lower-*.f64`
6 546×	`lower-*.f32`
4 326×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	757	12266
1	2433	11840
0	8237	11370

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 514

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)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (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)))
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(/ 1 x)
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1
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(/ (sin eps) (* x (cos eps)))
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(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (cos x) (sin x))) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 2/15 (/ (cos x) (sin x))) (+ (* 2/15 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (cos x) (sin x))) (* 17/315 (/ (sin x) (cos x))))))))))) (+ (/ (cos x) (sin x)) (/ (sin x) (cos x)))))
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(/ (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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 3)
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1 (* eps x))
(* eps (+ eps (* -1 x)))
(* eps (+ eps (* -1 x)))
(* eps (+ eps (* -1 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(pow eps 2)
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* -1 (* eps x)) (pow eps 2))
(* -1 (* eps x))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* -1 (* eps x))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
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)
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* -1/3 (pow x 2)) 1/2)
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -2/9 binary64) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -17/135 binary64) #s(literal -2/9 binary64)) #s(literal -1/3 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (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 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 binary64))) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 248/135 binary64) #s(literal 17/9 binary64)) #s(literal 4/3 binary64)) #s(literal 1/3 binary64))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (fma.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (neg.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(- (/ (sin (+ eps 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)))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* 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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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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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)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.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 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (/.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps))))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (/.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps))))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (.f64 eps (*.f64 eps eps)))
(* -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)))))
(.f64 (.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) 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)))))
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(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
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(+ eps (* 1/3 (pow eps 3)))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(fma.f64 x (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))
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x
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eps
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (/ (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 (/ (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 (/ (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 (/ (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 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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eps
(+ eps (* eps (pow x 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
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(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
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(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
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(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (cos x) (sin x))) (* 1/3 (/ (sin x) (cos x))))) (+ (/ (cos x) (sin x)) (/ (sin x) (cos x)))))
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(/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
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(+ (* 1/3 (pow eps 2)) (* eps x))
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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)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 13/120 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -41/3024 binary64) #s(literal 13/120 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (* eps x))
(*.f64 x (neg.f64 eps))
(* eps (+ eps (* -1 x)))
(*.f64 eps (-.f64 eps x))
(* eps (+ eps (* -1 x)))
(*.f64 eps (-.f64 eps x))
(* eps (+ eps (* -1 x)))
(*.f64 eps (-.f64 eps x))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(pow eps 2)
(*.f64 eps eps)
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(* -1 (* eps x))
(*.f64 x (neg.f64 eps))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(.f64 x (-.f64 (/.f64 (.f64 eps eps) x) eps))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(.f64 x (-.f64 (/.f64 (.f64 eps eps) x) eps))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(.f64 x (-.f64 (/.f64 (.f64 eps eps) x) eps))
(* -1 (* eps x))
(*.f64 x (neg.f64 eps))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(/ (* x (sin eps)) (cos eps))
(/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (.f64 x x) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 17/315 binary64) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(.f64 eps (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (/.f64 (sin.f64 x) (cos.f64 x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 17/315 binary64) (.f64 eps eps)) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))

rewrite271.0ms (1.7%)

Memory

-14.6MiB live, 328.2MiB allocated

Rules

4 908×	`lower-*.f32`
4 890×	`lower-*.f64`
4 716×	`lower-fma.f32`
4 698×	`lower-fma.f64`
2 340×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	548
0	120	481
1	542	362
2	4933	354
0	8173	344

Stop Event

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

Counts

26 → 592

Calls

Call 1

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

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

eval258.0ms (1.6%)

Memory: 8.2MiB live, 370.2MiB allocated
Compiler: Compiled 78 154 to 4 309 computations (94.5% saved)

prune233.0ms (1.5%)

Memory

-2.9MiB live, 311.5MiB allocated

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	1 494	17	1 511
Fresh	8	8	16
Picked	5	0	5
Done	0	1	1
Total	1 507	26	1 533

Accuracy

100.0%

Counts

1 533 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	62.5%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (sin.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
	62.1%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) #s(approx ( (- 1 (* (tan x) (tan eps))) (/ 1 (tan x))) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) eps)))
	63.7%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	98.3%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 14/45 binary64))) (.f64 #s(literal 2/3 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	99.0%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x))))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	39.5%	(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
	63.7%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	18.8%	(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
✓	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
▶	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))

Compiler

Compiled 1 169 to 590 computations (49.5% saved)

simplify270.0ms (1.7%)

Memory

16.4MiB live, 295.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))))
cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
cost-diff	128	(-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
cost-diff	128	(neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))
cost-diff	0	#s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x)))
cost-diff	0	(/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
cost-diff	0	(tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
cost-diff	0	(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
cost-diff	64	(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff	0	(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
cost-diff	0	(fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))
cost-diff	0	(fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))

Rules

15 300×	`lower-fma.f32`
15 282×	`lower-fma.f64`
4 418×	`lower-*.f32`
4 404×	`lower-*.f64`
2 572×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	1162
0	149	1136
1	272	1018
2	601	1015
3	1530	1015
4	5217	1015
0	8430	993

Stop Event

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

Calls

Call 1

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

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

localize312.0ms (2%)

Memory

10.0MiB live, 395.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1796875	(.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
accuracy	23.230795081529713	(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
accuracy	26.686643469065935	(/.f64 (*.f64 x x) (-.f64 x eps))
accuracy	27.053845316110095	(/.f64 (*.f64 eps eps) (-.f64 x eps))
accuracy	0.109375	(.f64 x (.f64 x x))
accuracy	3.578913138484654	#s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x)))
accuracy	23.230795081529713	(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
accuracy	39.44355161916248	(/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
accuracy	0.14453125	(*.f64 eps (+.f64 x eps))
accuracy	0.18359375	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	0.38721220768770737	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
accuracy	1.8692827274238255	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
accuracy	0	(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)
accuracy	0	(*.f64 x x)
accuracy	0.8947363595148837	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
accuracy	1.8030107668866597	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy	0.04982377930532605	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.125	(fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.38721220768770737	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	1.9000049197894051	#s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64))

Samples

97.0ms	87×	1	valid
88.0ms	166×	0	valid
3.0ms	2×	2	valid
2.0ms	1×	3	valid

Compiler

Compiled 906 to 74 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-mult: 29.0ms (18.7% of total)

ival-add: 26.0ms (16.7% of total)

adjust: 17.0ms (10.9% of total)

ival-div: 17.0ms (10.9% of total)

ival-tan: 15.0ms (9.7% of total)

const: 13.0ms (8.4% of total)

ival-pow2: 11.0ms (7.1% of total)

ival-pow: 10.0ms (6.4% of total)

ival-sub: 9.0ms (5.8% of total)

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

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

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

exact: 1.0ms (0.6% of total)

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

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

series132.0ms (0.8%)

Memory

-3.0MiB live, 156.9MiB allocated

Counts

28 → 600

Calls

Call 1

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

150 calls:

Time	Variable		Point	Expression
20.0ms	eps	@	inf	(- (/ (+ (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))) (- 1 (* (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))))) (tan x))
6.0ms	x	@	0	(* (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps)))))
6.0ms	x	@	-inf	(neg (/ (* eps eps) (- x eps)))
5.0ms	eps	@	0	(- (/ (+ (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))) (- 1 (* (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))))) (tan x))
4.0ms	x	@	inf	(- (/ (+ (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))) (- 1 (* (tan (/ (* x x) (- x eps))) (tan (neg (/ (* eps eps) (- x eps))))))) (tan x))

simplify616.0ms (3.9%)

Memory

-344.3MiB live, 381.4MiB allocated

Algorithm

1×	egg-herbie

Rules

5 608×	`lower-fma.f64`
5 608×	`lower-fma.f32`
5 380×	`lower-*.f64`
5 380×	`lower-*.f32`
3 680×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1667	24116
1	5700	23133
0	8272	22558

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 585

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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(* 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))))))
(* eps (- (+ 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))))))
(* eps (- (+ 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))))))
(* eps (- (+ 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))))))
(* 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))))))
(* -1 (* eps (+ (* -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 (* eps (+ (* -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 (* eps (+ (* -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)))))
(* 1/3 eps)
(+ x (* 1/3 eps))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(+ (* 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))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(pow x 2)
(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
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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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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(* 1/3 (pow eps 2))
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(/ (sin x) (cos x))
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eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
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x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))
(pow eps 3)
(+ (pow eps 3) (pow x 3))
(+ (pow eps 3) (pow x 3))
(+ (pow eps 3) (pow x 3))
(pow x 3)
(* (pow x 3) (+ 1 (/ (pow eps 3) (pow x 3))))
(* (pow x 3) (+ 1 (/ (pow eps 3) (pow x 3))))
(* (pow x 3) (+ 1 (/ (pow eps 3) (pow x 3))))
(pow x 3)
(* -1 (* (pow x 3) (- (* -1 (/ (pow eps 3) (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (pow eps 3) (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (pow eps 3) (pow x 3))) 1)))
(pow x 3)
(+ (pow eps 3) (pow x 3))
(+ (pow eps 3) (pow x 3))
(+ (pow eps 3) (pow x 3))
(pow eps 3)
(* (pow eps 3) (+ 1 (/ (pow x 3) (pow eps 3))))
(* (pow eps 3) (+ 1 (/ (pow x 3) (pow eps 3))))
(* (pow eps 3) (+ 1 (/ (pow x 3) (pow eps 3))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (pow x 3) (pow eps 3))) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (pow x 3) (pow eps 3))) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (pow x 3) (pow eps 3))) 1)))
(* -1 (/ (pow eps 2) x))
(* (pow eps 2) (- (* -1 (/ eps (pow x 2))) (/ 1 x)))
(* (pow eps 2) (- (* eps (- (* -1 (/ eps (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))
(* (pow eps 2) (- (* eps (- (* eps (- (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))
(* eps (+ 1 (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (+ x (/ (pow x 2) eps)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2))) eps))) eps)) 1)))
eps
(- x (* -1 eps))
(- (* x (+ 1 (/ x eps))) (* -1 eps))
(- (* x (+ 1 (* x (+ (/ 1 eps) (/ x (pow eps 2)))))) (* -1 eps))
(* -1 (/ (pow eps 2) x))
(/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)
(/ (- (+ (* -1 (/ (pow eps 3) x)) (* -1 (/ (pow eps 4) (pow x 2)))) (pow eps 2)) x)
(/ (- (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (* -1 (/ (pow eps 5) (pow x 3))))) (pow eps 2)) x)
(* -1 (/ (pow eps 2) x))
(* -1 (/ (- (/ (pow eps 3) x) (* -1 (pow eps 2))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 4) x)) (pow eps 3)) x)) (* -1 (pow eps 2))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow eps 5) x) (* -1 (pow eps 4))) x)) (pow eps 3)) x)) (* -1 (pow eps 2))) x))
1
(+ 1 (/ (* (pow x 2) (sin (neg (* -1 eps)))) (* eps (cos (neg (* -1 eps))))))
(+ 1 (* (pow x 2) (- (* -1 (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 2) (cos (neg (* -1 eps)))))) (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) eps))))) (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))))))
(+ 1 (* (pow x 2) (- (* x (- (* -1 (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 3) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (pow eps 2))) (* -1 (/ (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)))) eps)))))) (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 2) (cos (neg (* -1 eps)))))) (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) eps))))) (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))))))
1
(+ 1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps))))))
(- (+ 1 (/ (* (pow eps 3) (sin (/ (pow x 2) (- x eps)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps)))))) (* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps)))))))
(- (+ 1 (* -1 (/ (* (sin (/ (pow x 2) (- x eps))) (- (+ (* -1 (pow eps 4)) (* 1/6 (pow eps 6))) (* 1/2 (pow eps 6)))) (* (pow x 3) (cos (/ (pow x 2) (- x eps))))))) (+ (* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps)))))) (* -1 (/ (* (pow eps 3) (sin (/ (pow x 2) (- x eps)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps))))))))
1
(+ 1 (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))))
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow eps 3) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) x)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (- (+ (* -1/6 (pow eps 6)) (pow eps 4)) (* -1/2 (pow eps 6)))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (* -1 (/ (* (pow eps 3) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) x)) (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) x)))
1
(+ 1 (/ (* (pow eps 2) (sin x)) (* x (cos x))))
(+ 1 (* (pow eps 2) (- (* -1 (* eps (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))) (* -1 (/ (sin x) (* x (cos x)))))))
(+ 1 (* (pow eps 2) (- (* eps (- (* -1 (* eps (+ (* -1 (/ (sin x) (* (pow x 3) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow x 2))) (* -1 (/ (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)))) x)))))) (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))) (* -1 (/ (sin x) (* x (cos x)))))))
1
(+ 1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps)))))))
(- (+ 1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps))))))) (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))))
(- (+ 1 (* -1 (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (+ (* -1 (pow x 4)) (* 1/6 (pow x 6))) (* 1/2 (pow x 6)))) (* (pow eps 3) (cos (neg (/ (pow eps 2) (- x eps)))))))) (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps)))))))))
1
(+ 1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))))
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (+ (* -1/6 (pow x 6)) (pow x 4)) (* -1/2 (pow x 6)))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) eps)) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps)))
(/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))
(+ (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps)))) (/ (* x (pow (sin (neg (* -1 eps))) 2)) (pow (cos (neg (* -1 eps))) 2)))
(+ (* x (- (* x (- (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (+ (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)) (/ (pow (sin (neg (* -1 eps))) 2) (* eps (pow (cos (neg (* -1 eps))) 2))))))) (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps)))))
(+ (* x (- (* x (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (* x (- (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))) (+ 1/2 (+ (* -1 (/ (* (sin (neg (* -1 eps))) (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 2) (cos (neg (* -1 eps)))))) (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) eps)))) (cos (neg (* -1 eps))))) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (+ (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (* eps (cos (neg (* -1 eps))))) (+ (/ (* (sin (neg (* -1 eps))) (- (* -1 (/ (cos (neg (* -1 eps))) eps)) (* (sin (neg (* -1 eps))) (- (/ 1 (pow eps 2)) 1/6)))) (pow (cos (neg (* -1 eps))) 2)) (/ (* (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (cos (neg (* -1 eps)))))))))))) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (+ (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)) (/ (pow (sin (neg (* -1 eps))) 2) (* eps (pow (cos (neg (* -1 eps))) 2))))))) (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps)))))
(- (/ (sin (/ (pow x 2) (- x eps))) (cos (/ (pow x 2) (- x eps)))) (/ (sin x) (cos x)))
(- (+ (* -1 (/ (pow eps 2) x)) (/ (sin (/ (pow x 2) (- x eps))) (cos (/ (pow x 2) (- x eps))))) (+ (/ (sin x) (cos x)) (/ (* (pow eps 2) (pow (sin (/ (pow x 2) (- x eps))) 2)) (* x (pow (cos (/ (pow x 2) (- x eps))) 2)))))
(- (+ (* -1 (/ (pow eps 2) x)) (+ (* -1 (/ (pow eps 3) (pow x 2))) (/ (sin (/ (pow x 2) (- x eps))) (cos (/ (pow x 2) (- x eps)))))) (+ (* -1 (/ (* (pow eps 4) (sin (/ (pow x 2) (- x eps)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps)))))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (/ (pow x 2) (- x eps))) 3)) (* (pow x 2) (pow (cos (/ (pow x 2) (- x eps))) 3)))) (+ (/ (sin x) (cos x)) (+ (/ (* (pow eps 2) (pow (sin (/ (pow x 2) (- x eps))) 2)) (* x (pow (cos (/ (pow x 2) (- x eps))) 2))) (/ (* (pow eps 3) (pow (sin (/ (pow x 2) (- x eps))) 2)) (* (pow x 2) (pow (cos (/ (pow x 2) (- x eps))) 2))))))))
(- (+ (* -1 (/ (pow eps 2) x)) (+ (* -1 (/ (pow eps 3) (pow x 2))) (+ (* -1 (/ (pow eps 4) (pow x 3))) (+ (* 1/6 (/ (pow eps 6) (pow x 3))) (/ (sin (/ (pow x 2) (- x eps))) (cos (/ (pow x 2) (- x eps)))))))) (+ (* -1 (/ (* (pow eps 2) (* (sin (/ (pow x 2) (- x eps))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (/ (pow x 2) (- x eps))) 3)) (pow (cos (/ (pow x 2) (- x eps))) 3))) (/ (* (pow eps 3) (pow (sin (/ (pow x 2) (- x eps))) 2)) (pow (cos (/ (pow x 2) (- x eps))) 2))))) (* (pow x 3) (cos (/ (pow x 2) (- x eps)))))) (+ (* -1 (/ (* (pow eps 4) (sin (/ (pow x 2) (- x eps)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps)))))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (/ (pow x 2) (- x eps))) 3)) (* (pow x 2) (pow (cos (/ (pow x 2) (- x eps))) 3)))) (+ (* -1 (/ (* (pow eps 5) (sin (/ (pow x 2) (- x eps)))) (* (pow x 3) (cos (/ (pow x 2) (- x eps)))))) (+ (* -1 (/ (* (pow eps 5) (pow (sin (/ (pow x 2) (- x eps))) 3)) (* (pow x 3) (pow (cos (/ (pow x 2) (- x eps))) 3)))) (+ (* -1 (/ (* (pow (sin (/ (pow x 2) (- x eps))) 2) (- (+ (* -1 (pow eps 4)) (* 1/6 (pow eps 6))) (* 1/2 (pow eps 6)))) (* (pow x 3) (pow (cos (/ (pow x 2) (- x eps))) 2)))) (+ (* 1/2 (/ (pow eps 6) (pow x 3))) (+ (/ (sin x) (cos x)) (+ (/ (* (pow eps 2) (* (sin (/ (pow x 2) (- x eps))) (- (* -1 (pow eps 3)) (* -1 (/ (* (pow eps 4) (sin (/ (pow x 2) (- x eps)))) (cos (/ (pow x 2) (- x eps)))))))) (* (pow x 3) (cos (/ (pow x 2) (- x eps))))) (+ (/ (* (pow eps 2) (pow (sin (/ (pow x 2) (- x eps))) 2)) (* x (pow (cos (/ (pow x 2) (- x eps))) 2))) (/ (* (pow eps 3) (pow (sin (/ (pow x 2) (- x eps))) 2)) (* (pow x 2) (pow (cos (/ (pow x 2) (- x eps))) 2))))))))))))))
(- (/ (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (/ (sin x) (cos x)))
(- (+ (* -1 (/ (- (pow eps 2) (* -1 (/ (* (pow eps 2) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)))) x)) (/ (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (/ (sin x) (cos x)))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (pow eps 3)) (+ (* -1 (/ (* (pow eps 4) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3))) (/ (* (pow eps 3) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2))))) x)) (pow eps 2)) (* -1 (/ (* (pow eps 2) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)))) x)) (/ (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (/ (sin x) (cos x)))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/6 (pow eps 6)) (pow eps 4)) (+ (* -1 (/ (* (pow eps 2) (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (- (* -1 (pow eps 3)) (* -1 (/ (* (pow eps 4) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (+ (* -1 (/ (* (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2) (- (+ (* -1/6 (pow eps 6)) (pow eps 4)) (* -1/2 (pow eps 6)))) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2))) (+ (* -1/2 (pow eps 6)) (+ (/ (* (pow eps 2) (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3))) (/ (* (pow eps 3) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (+ (/ (* (pow eps 5) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (/ (* (pow eps 5) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3)))))))) x)) (* -1 (pow eps 3))) (+ (* -1 (/ (* (pow eps 4) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (+ (* -1 (/ (* (pow eps 4) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 3))) (/ (* (pow eps 3) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2))))) x)) (pow eps 2)) (* -1 (/ (* (pow eps 2) (pow (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)) (pow (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))) 2)))) x)) (/ (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1/2 (/ (sin x) (cos x))) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* x (pow (cos x) 2)))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* eps (- (* -1 (/ (sin x) (* x (cos x)))) (+ 1/6 (+ (* -1 (/ (* (sin x) (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) (cos x))) (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2))))) (cos x))) (+ (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* x (cos x))) (+ (/ (* (sin x) (- (* -1 (/ (cos x) x)) (* (sin x) (- (/ 1 (pow x 2)) 1/6)))) (pow (cos x) 2)) (/ (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* -1/2 (cos x)) (/ (sin x) x))) (cos x)))))))))) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* x (pow (cos x) 2)))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))
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(/ (sin (neg (/ (pow eps 2) (- x eps)))) (cos (neg (/ (pow eps 2) (- x eps)))))
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(/ (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))
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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)))))
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(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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)))))
(pow x 3)
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(* 1/3 (pow eps 2))
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(pow eps 2)
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(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(pow x 3)
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(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
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(/ (pow eps 2) x)
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(* (pow eps 2) (+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x)))
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(* -1 eps)
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(* -1 eps)
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(/ (pow eps 2) x)
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x
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x
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x
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(/ (- (+ (* -1 (/ (pow x 5) (pow eps 3))) (* -1 (pow x 2))) (+ (/ (pow x 3) eps) (/ (pow x 4) (pow eps 2)))) eps)
(* -1 (/ (pow x 2) eps))
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(* -1 (/ (* (pow x 2) (sin (neg (* -1 eps)))) (* eps (cos (neg (* -1 eps))))))
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(* (pow x 2) (+ (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))) (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 2) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) eps)) (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 3) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (pow eps 2))) (* -1 (/ (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)))) eps))))))))))
(* (pow x 2) (+ (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))) (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 2) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) eps)) (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 3) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (pow eps 2))) (+ (* -1 (/ (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)))) eps)) (* x (+ (* -1 (/ (sin (neg (* -1 eps))) (* (pow eps 4) (cos (neg (* -1 eps)))))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (pow eps 3))) (+ (* -1 (/ (- (+ (* -1 (/ (sin (neg (* -1 eps))) (* eps (cos (neg (* -1 eps)))))) (/ 1 (pow eps 2))) (+ 1/6 (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (+ (/ (* (sin (neg (* -1 eps))) (- (* -1 (/ (cos (neg (* -1 eps))) eps)) (* (sin (neg (* -1 eps))) (- (/ 1 (pow eps 2)) 1/6)))) (pow (cos (neg (* -1 eps))) 2)) (/ (* (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2)))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (cos (neg (* -1 eps)))))))) eps)) (* -1 (/ (- (+ (* -1/2 (/ (sin (neg (* -1 eps))) (cos (neg (* -1 eps))))) (/ 1 eps)) (+ (* -1 (/ (* (sin (neg (* -1 eps))) (- 1 (* -1 (/ (pow (sin (neg (* -1 eps))) 2) (pow (cos (neg (* -1 eps))) 2))))) (cos (neg (* -1 eps))))) (/ (* (sin (neg (* -1 eps))) (- (* -1/2 (cos (neg (* -1 eps)))) (/ (sin (neg (* -1 eps))) eps))) (pow (cos (neg (* -1 eps))) 2)))) (pow eps 2))))))))))))))))
(* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps))))))
(/ (+ (* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (cos (/ (pow x 2) (- x eps))))) (* -1 (/ (* (pow eps 3) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps))))))) x)
(/ (+ (* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (cos (/ (pow x 2) (- x eps))))) (+ (* -1 (/ (* (pow eps 3) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps)))))) (/ (* (sin (/ (pow x 2) (- x eps))) (- (+ (* -1 (pow eps 4)) (* 1/6 (pow eps 6))) (* 1/2 (pow eps 6)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps))))))) x)
(/ (+ (* -1 (/ (* (pow eps 2) (sin (/ (pow x 2) (- x eps)))) (cos (/ (pow x 2) (- x eps))))) (+ (* -1 (/ (* (pow eps 3) (sin (/ (pow x 2) (- x eps)))) (* x (cos (/ (pow x 2) (- x eps)))))) (+ (/ (* (sin (/ (pow x 2) (- x eps))) (- (* -1 (pow eps 5)) (pow eps 7))) (* (pow x 3) (cos (/ (pow x 2) (- x eps))))) (/ (* (sin (/ (pow x 2) (- x eps))) (- (+ (* -1 (pow eps 4)) (* 1/6 (pow eps 6))) (* 1/2 (pow eps 6)))) (* (pow x 2) (cos (/ (pow x 2) (- x eps)))))))) x)
(* -1 (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))))
(* -1 (/ (+ (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (/ (* (pow eps 3) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (- (+ (* -1/6 (pow eps 6)) (pow eps 4)) (* -1/2 (pow eps 6)))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) (* -1 (/ (* (pow eps 3) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) x)) (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow eps 3) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) (* -1 (/ (+ (* -1 (/ (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (- (* -1 (pow eps 5)) (pow eps 7))) (* x (cos (* -1 (/ (pow x 2) (+ eps (* -1 x)))))))) (/ (* (sin (* -1 (/ (pow x 2) (+ eps (* -1 x))))) (- (+ (* -1/6 (pow eps 6)) (pow eps 4)) (* -1/2 (pow eps 6)))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) x))) x)) (/ (* (pow eps 2) (sin (* -1 (/ (pow x 2) (+ eps (* -1 x)))))) (cos (* -1 (/ (pow x 2) (+ eps (* -1 x))))))) x))
(* -1 (/ (* (pow eps 2) (sin x)) (* x (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (* x (cos x)))) (* eps (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (* x (cos x)))) (* eps (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* eps (+ (* -1 (/ (sin x) (* (pow x 3) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow x 2))) (* -1 (/ (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)))) x))))))))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (* x (cos x)))) (* eps (+ (* -1 (/ (sin x) (* (pow x 2) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* eps (+ (* -1 (/ (sin x) (* (pow x 3) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow x 2))) (+ (* -1 (/ (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)))) x)) (* eps (+ (* -1 (/ (sin x) (* (pow x 4) (cos x)))) (+ (* -1 (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow x 3))) (+ (* -1 (/ (- (+ (* -1 (/ (sin x) (* x (cos x)))) (/ 1 (pow x 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2))))) (cos x))) (+ (/ (* (sin x) (- (* -1 (/ (cos x) x)) (* (sin x) (- (/ 1 (pow x 2)) 1/6)))) (pow (cos x) 2)) (/ (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* -1/2 (cos x)) (/ (sin x) x))) (cos x)))))) x)) (* -1 (/ (- (+ (* -1/2 (/ (sin x) (cos x))) (/ 1 x)) (+ (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (- (* -1/2 (cos x)) (/ (sin x) x))) (pow (cos x) 2)))) (pow x 2))))))))))))))))
(* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps)))))))
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps)))))))) eps)
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))) (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (+ (* -1 (pow x 4)) (* 1/6 (pow x 6))) (* 1/2 (pow x 6)))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps)))))))) eps)
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))) (+ (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (* -1 (pow x 5)) (pow x 7))) (* (pow eps 3) (cos (neg (/ (pow eps 2) (- x eps)))))) (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (+ (* -1 (pow x 4)) (* 1/6 (pow x 6))) (* 1/2 (pow x 6)))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps))))))))) eps)
(* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))))
(* -1 (/ (+ (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (+ (* -1/6 (pow x 6)) (pow x 4)) (* -1/2 (pow x 6)))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) eps)) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) (* -1 (/ (+ (* -1 (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (* -1 (pow x 5)) (pow x 7))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (+ (* -1/6 (pow x 6)) (pow x 4)) (* -1/2 (pow x 6)))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))) eps)) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (/.f64 (*.f64 (sin.f64 eps) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (fma.f64 (neg.f64 x) (+.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 eps) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 (neg.f64 eps) (+.f64 #s(literal 1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))) #s(literal -1/6 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 eps (*.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (+ 1 (+ (* 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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(* 1/3 (pow eps 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)))
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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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(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
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(+ (* 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))))
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(+ (* 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))))
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(+ (* 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))))
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(* 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))))))
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(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (-.f64 (+.f64 (+.f64 #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)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) (.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))))
(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (-.f64 (+.f64 (+.f64 #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)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) (.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))))
(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (-.f64 (+.f64 (+.f64 #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)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) (.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))))
(* 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))))))
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(* -1 (* eps (+ (* -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 (* eps (+ (* -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 (* eps (+ (* -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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(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(+ x (* 1/3 eps))
(fma.f64 eps #s(literal 1/3 binary64) x)
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps x) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))
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(+ (* 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))))
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(+ (* 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))))
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(+ (* 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))))
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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 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
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(+ (* 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)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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eps
(+ eps (* eps (pow x 2)))
(fma.f64 eps (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal -1/3 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 2/45 binary64)) (-.f64 (.f64 eps #s(literal 1/3 binary64)) (.f64 eps #s(literal 2/3 binary64)))) eps)) eps) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
eps
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) eps)
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) eps)
(* 4/3 (* eps (pow x 2)))
(.f64 #s(literal 4/3 binary64) (.f64 eps (*.f64 x x)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 eps #s(literal 4/3 binary64) (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 eps #s(literal 4/3 binary64) (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 eps (.f64 x x)))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 eps #s(literal 4/3 binary64) (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 eps (.f64 x x)))))
(* 4/3 (* eps (pow x 2)))
(.f64 #s(literal 4/3 binary64) (.f64 eps (*.f64 x x)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 eps #s(literal 4/3 binary64) (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 4/3 binary64)) (/.f64 (-.f64 (/.f64 (neg.f64 eps) x) (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x)))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) x)
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) x)
(* 4/3 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 4/3 binary64) (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 4/3 binary64) (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (.f64 eps eps)))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 4/3 binary64) (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (.f64 eps eps)))))
(* 4/3 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x)))
(.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) (/.f64 (neg.f64 x) eps)) #s(literal -1 binary64)) eps)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) (/.f64 (neg.f64 x) eps)) #s(literal -1 binary64)) eps)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
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(+ (* 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 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 eps (*.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
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eps
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eps
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(- (* x (+ 1 (/ x eps))) (* -1 eps))
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(- (* x (+ 1 (* x (+ (/ 1 eps) (/ x (pow eps 2)))))) (* -1 eps))
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(* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps)))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps)))))))) eps)
(neg.f64 (/.f64 (fma.f64 (.f64 x x) (/.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) eps))
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))) (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (+ (* -1 (pow x 4)) (* 1/6 (pow x 6))) (* 1/2 (pow x 6)))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps)))))))) eps)
(/.f64 (+.f64 (neg.f64 (fma.f64 (.f64 x x) (/.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))))) (/.f64 (.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (+.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (.f64 eps eps) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))) eps)
(/ (+ (* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (- x eps))))) (cos (neg (/ (pow eps 2) (- x eps)))))) (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (- x eps))))) (* eps (cos (neg (/ (pow eps 2) (- x eps))))))) (+ (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (* -1 (pow x 5)) (pow x 7))) (* (pow eps 3) (cos (neg (/ (pow eps 2) (- x eps)))))) (/ (* (sin (neg (/ (pow eps 2) (- x eps)))) (- (+ (* -1 (pow x 4)) (* 1/6 (pow x 6))) (* 1/2 (pow x 6)))) (* (pow eps 2) (cos (neg (/ (pow eps 2) (- x eps))))))))) eps)
(/.f64 (+.f64 (neg.f64 (fma.f64 (.f64 x x) (/.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))))) (fma.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (/.f64 (-.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 7 binary64))) (.f64 (.f64 eps (.f64 eps eps)) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (/.f64 (.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (+.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (.f64 eps eps) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) eps)
(* -1 (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(* -1 (/ (+ (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) eps))
(neg.f64 (/.f64 (fma.f64 (.f64 x x) (/.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (.f64 eps (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (+ (* -1/6 (pow x 6)) (pow x 4)) (* -1/2 (pow x 6)))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) eps)) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))
(neg.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (neg.f64 (/.f64 (fma.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (/.f64 (+.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 eps (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) eps))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) (* -1 (/ (+ (* -1 (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (* -1 (pow x 5)) (pow x 7))) (* eps (cos (neg (/ (pow eps 2) (+ x (* -1 eps)))))))) (/ (* (sin (neg (/ (pow eps 2) (+ x (* -1 eps))))) (- (+ (* -1/6 (pow x 6)) (pow x 4)) (* -1/2 (pow x 6)))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))) eps)) (/ (* (pow x 2) (sin (neg (/ (pow eps 2) (+ x (* -1 eps)))))) (cos (neg (/ (pow eps 2) (+ x (* -1 eps))))))) eps))
(neg.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps)))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (-.f64 (/.f64 (.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (+.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (/.f64 (.f64 (sin.f64 (/.f64 (neg.f64 (.f64 eps eps)) (-.f64 x eps))) (-.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 7 binary64)))) (.f64 eps (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))) eps))) eps)) eps))

rewrite316.0ms (2%)

Memory

8.8MiB live, 396.8MiB allocated

Rules

6 446×	`lower-fma.f32`
6 428×	`lower-fma.f64`
5 742×	`lower-*.f32`
5 728×	`lower-*.f64`
2 712×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	989
0	149	963
1	642	747
2	5757	747
0	9179	715

Stop Event

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

Counts

28 → 407

Calls

Call 1

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

eval185.0ms (1.2%)

Memory: 28.2MiB live, 319.3MiB allocated
Compiler: Compiled 58 504 to 3 948 computations (93.3% saved)

prune207.0ms (1.3%)

Memory

-22.9MiB live, 385.2MiB allocated

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	1 167	12	1 179
Fresh	7	13	20
Picked	3	2	5
Done	0	1	1
Total	1 177	28	1 205

Accuracy

100.0%

Counts

1 205 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	63.7%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	39.5%	(-.f64 (/.f64 (-.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) #s(literal 1 binary64))) (tan.f64 x))
	63.7%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	18.8%	(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
✓	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	62.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
▶	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
✓	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) #s(approx (* eps (+ x eps)) (.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	96.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 #s(literal 4/3 binary64) (.f64 eps (.f64 x x)))) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
▶	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))

Compiler

Compiled 1 142 to 579 computations (49.3% saved)

simplify294.0ms (1.9%)

Memory

-5.5MiB live, 344.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	0	#s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
cost-diff	0	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))
cost-diff	0	(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
cost-diff	0	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff	0	(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
cost-diff	128	(.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
cost-diff	6272	(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
cost-diff	6400	(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))))

Rules

24 652×	`lower-fma.f32`
24 628×	`lower-fma.f64`
4 472×	`lower-*.f32`
4 460×	`lower-*.f64`
2 528×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1132
0	136	1124
1	249	984
2	562	980
3	1382	980
4	3949	980
5	7155	980
0	8199	952

Stop Event

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

Calls

Call 1

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

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

localize312.0ms (2%)

Memory

25.5MiB live, 381.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.12109375	(fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.38721220768770737	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	1.924768594518129	#s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))
accuracy	0.0585384450664193	(tan.f64 (+.f64 x eps))
accuracy	0.109375	(.f64 x (.f64 x x))
accuracy	0.842967448151178	#s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x))
accuracy	23.226888831529713	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
accuracy	0.015625	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
accuracy	0.02734375	(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
accuracy	0.8094969639306885	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))))
accuracy	0.8947363595148837	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
accuracy	0	(*.f64 x x)
accuracy	0.04296875	(.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps)
accuracy	0.8947363595148837	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
accuracy	1.8030107668866597	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy	0.02734375	(fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))
accuracy	0.1484375	(.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))
accuracy	0.38721220768770737	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
accuracy	1.9000049197894051	#s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64))

Samples

99.0ms	171×	0	valid
93.0ms	84×	1	valid
3.0ms	1×	5	exit

Compiler

Compiled 848 to 77 computations (90.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 162.0ms

ival-mult: 46.0ms (28.5% of total)

ival-add: 33.0ms (20.4% of total)

const: 21.0ms (13% of total)

adjust: 14.0ms (8.7% of total)

ival-div: 13.0ms (8% of total)

ival-pow: 10.0ms (6.2% of total)

ival-pow2: 9.0ms (5.6% of total)

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

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

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

ival-sin: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series102.0ms (0.7%)

Memory

-14.5MiB live, 64.5MiB allocated

Counts

27 → 504

Calls

Call 1

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

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

Calls

126 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))))
2.0ms	x	@	inf	(+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))))
1.0ms	eps	@	0	(+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))))
1.0ms	eps	@	0	(* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))
0.0ms	eps	@	0	(* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps)

simplify301.0ms (1.9%)

Memory

22.8MiB live, 339.1MiB allocated

Algorithm

1×	egg-herbie

Rules

8 838×	`lower-fma.f64`
8 838×	`lower-fma.f32`
6 084×	`lower-*.f64`
6 084×	`lower-*.f32`
3 176×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	13117
1	1395	12757
2	4578	12438
0	8092	11921

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 494

Calls

Call 1

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

Outputs
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 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) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(* (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 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (.f64 eps (cos.f64 x))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (.f64 eps (cos.f64 x))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))))
(* (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 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 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 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) 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 (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 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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x
(* x (+ 1 (* 5/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
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(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
x
(+ eps x)
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(+ eps x)
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(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 x (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
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(/ (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))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* 1/3 (pow eps 2))
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(* 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))))))
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(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* eps (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ x (* 1/3 eps))
(fma.f64 #s(literal 1/3 binary64) eps x)
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(fma.f64 #s(literal 1/3 binary64) eps (fma.f64 x (.f64 (.f64 eps x) #s(literal 4/3 binary64)) x))
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(fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))
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1/3
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(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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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)))))
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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)))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (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 (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (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 (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x)))))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 (.f64 eps eps) (.f64 x #s(literal 4/3 binary64)) eps)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 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)))))
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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)))))
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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)))))
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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)))))
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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)))))
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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)))))
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(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

rewrite306.0ms (2%)

Memory

31.0MiB live, 409.3MiB allocated

Rules

6 588×	`lower-fma.f32`
6 564×	`lower-fma.f64`
5 240×	`lower-*.f32`
5 228×	`lower-*.f64`
2 220×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	926
0	136	924
1	611	665
2	5514	665
0	8471	641

Stop Event

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

Counts

27 → 426

Calls

Call 1

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

Outputs
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(+.f64 (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(+.f64 (.f64 #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (.f64 eps eps)) (fma.f64 eps (/.f64 (.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (.f64 eps eps))) (/.f64 (.f64 eps (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))) (/.f64 (pow.f64 (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))))
(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 (sin.f64 x) (pow.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 eps (.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64))) (fma.f64 eps (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 eps (/.f64 (.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (tan.f64 x) (tan.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))))
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eval173.0ms (1.1%)

Memory: -22.9MiB live, 289.9MiB allocated
Compiler: Compiled 36 388 to 2 141 computations (94.1% saved)

prune240.0ms (1.5%)

Memory

45.1MiB live, 319.5MiB allocated

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	1 005	15	1 020
Fresh	8	12	20
Picked	3	2	5
Done	1	2	3
Total	1 017	31	1 048

Accuracy

100.0%

Counts

1 048 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.6%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	39.5%	(-.f64 (/.f64 (-.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) #s(literal 1 binary64))) (tan.f64 x))
	63.7%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	62.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (.f64 x (*.f64 x x)) x)) (cos.f64 x))))) eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 277/1008 binary64) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))))) eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
✓	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
✓	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) #s(approx (* eps (+ x eps)) (.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	96.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 #s(literal 4/3 binary64) (.f64 eps (.f64 x x)))) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))

Compiler

Compiled 2 255 to 705 computations (68.7% saved)

regimes70.0ms (0.4%)

Memory

-17.7MiB live, 100.8MiB allocated

Counts

66 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

26.0ms	x
20.0ms	eps
16.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes61.0ms (0.4%)

Memory

18.6MiB live, 90.7MiB allocated

Counts

65 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 #s(literal 4/3 binary64) (.f64 eps (.f64 x x)))) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) #s(approx (* eps (+ x eps)) (.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))) eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (.f64 x (*.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 277/1008 binary64) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (sin.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(-.f64 (/.f64 (-.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) #s(approx ( (- 1 (* (tan x) (tan eps))) (/ 1 (tan x))) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x))))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (/ 1 (tan x))) (* (- 1 (* (tan x) (tan eps))) 1)) (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 14/45 binary64))) (.f64 #s(literal 2/3 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))))

Outputs

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

Calls

3 calls:

21.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20.0ms	x
16.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes80.0ms (0.5%)

Memory

-50.9MiB live, 63.5MiB allocated

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 #s(literal 4/3 binary64) (.f64 eps (.f64 x x)))) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) #s(approx (* eps (+ x eps)) (.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))) eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (.f64 x (*.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 277/1008 binary64) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (sin.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(-.f64 (/.f64 (-.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) #s(approx ( (- 1 (* (tan x) (tan eps))) (/ 1 (tan x))) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) eps)))

Outputs

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

Calls

3 calls:

45.0ms	x
18.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms	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)

regimes48.0ms (0.3%)

Memory

23.7MiB live, 61.0MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 #s(literal 4/3 binary64) (.f64 eps (.f64 x x)))) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) #s(approx (* eps (+ x eps)) (.f64 eps x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* (sin x) (/ (sin x) (+ 1/2 (* 1/2 (cos (+ x x)))))) (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x #s(approx (+ (* x (+ (* 4/3 (* eps (+ x eps))) 1)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 4/3 binary64)) (/.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1 binary64)) eps)))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
(-.f64 (tan.f64 (/.f64 #s(approx (+ (* x (* x x)) (* eps (* eps eps))) (.f64 x (.f64 x x))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (tan.f64 x))
(-.f64 (tan.f64 (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -2/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))))) eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (.f64 x (*.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 277/1008 binary64) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (sin.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(-.f64 (/.f64 (-.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (tan.f64 (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))) (tan.f64 x))

Outputs

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

Calls

3 calls:

18.0ms	eps
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Memory

-16.8MiB live, 58.3MiB allocated

Counts

45 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	x
16.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes40.0ms (0.3%)

Memory

13.2MiB live, 58.6MiB allocated

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

17.0ms	eps
10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Memory

-5.7MiB live, 31.5MiB allocated

Counts

31 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

27.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps
8.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.3%)

Memory

-7.8MiB live, 29.8MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))

Calls

3 calls:

33.0ms	eps
8.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

6.3MiB live, 43.5MiB allocated

Counts

27 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

11.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

24.3MiB live, 24.3MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

-24.2MiB live, 21.8MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-26.9MiB live, 11.1MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`
97.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) 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
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify18.0ms (0.1%)

Memory

-13.4MiB live, 24.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	826
1	177	826
2	181	826
3	183	826
4	184	826

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ ( 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (.f64 #s(literal 5/6 binary64) (.f64 x x)) x)) (cos.f64 x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 eps #s(approx (+ ( eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x))) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 eps #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) x) x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 eps #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 eps #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64))))

soundness1.6s (10.2%)

Memory

16.4MiB live, 973.8MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
9 960×	`lower-fma.f64`
9 960×	`lower-fma.f32`
8 838×	`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	64	548
0	120	481
1	542	362
2	4933	354
0	8173	344
0	445	13117
1	1395	12757
2	4578	12438
0	8092	11921
0	82	926
0	136	924
1	611	665
2	5514	665
0	8471	641
0	91	989
0	149	963
1	642	747
2	5757	747
0	9179	715
0	1667	24116
1	5700	23133
0	8272	22558
0	757	12266
1	2433	11840
0	8237	11370

Stop Event

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

Compiler

Compiled 753 to 332 computations (55.9% saved)

preprocess190.0ms (1.2%)

Memory: -13.4MiB live, 182.9MiB allocated
Compiler: Compiled 752 to 248 computations (67% 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%)

analyze40.0ms (0.3%)

sample6.9s (44%)

explain159.0ms (1%)

preprocess47.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize43.0ms (0.3%)

series33.0ms (0.2%)

simplify336.0ms (2.1%)

rewrite244.0ms (1.6%)

eval40.0ms (0.3%)

prune64.0ms (0.4%)

simplify229.0ms (1.5%)

localize296.0ms (1.9%)

series109.0ms (0.7%)

simplify283.0ms (1.8%)

rewrite271.0ms (1.7%)

eval258.0ms (1.6%)

prune233.0ms (1.5%)

simplify270.0ms (1.7%)

localize312.0ms (2%)

series132.0ms (0.8%)

simplify616.0ms (3.9%)

rewrite316.0ms (2%)

eval185.0ms (1.2%)

prune207.0ms (1.3%)

simplify294.0ms (1.9%)

localize312.0ms (2%)

series102.0ms (0.7%)

simplify301.0ms (1.9%)

rewrite306.0ms (2%)

eval173.0ms (1.1%)

prune240.0ms (1.5%)

regimes70.0ms (0.4%)

regimes61.0ms (0.4%)

regimes80.0ms (0.5%)

regimes48.0ms (0.3%)

regimes46.0ms (0.3%)

regimes40.0ms (0.3%)

regimes46.0ms (0.3%)

regimes51.0ms (0.3%)

regimes28.0ms (0.2%)

regimes13.0ms (0.1%)

regimes16.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes4.0ms (0%)

simplify18.0ms (0.1%)

soundness1.6s (10.2%)

preprocess190.0ms (1.2%)

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