Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze71.0ms (0.5%)

Memory

4.1MiB live, 79.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.6s (43.3%)

Memory

-189.0MiB live, 7 830.9MiB allocated

Samples

3.4s	26 194×	0	invalid
702.0ms	2 781×	1	valid
698.0ms	5 475×	0	valid

Precisions

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

const: 862.0ms (25.2% of total)

ival-tan: 633.0ms (18.5% of total)

ival-mult: 330.0ms (9.6% of total)

ival-fabs: 322.0ms (9.4% of total)

ival-add: 285.0ms (8.3% of total)

ival-<: 272.0ms (7.9% of total)

ival-<=: 270.0ms (7.9% of total)

ival-sub: 197.0ms (5.7% of total)

adjust: 106.0ms (3.1% of total)

ival-and: 98.0ms (2.9% of total)

exact: 42.0ms (1.2% of total)

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

Bogosity

explain120.0ms (0.8%)

Memory

-14.4MiB live, 114.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
216	2	(2.3794404783451385e-103 2.258794647997274e-105)	2	(-2.2077112374028354e-243 6.6877552078313866e-245)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
6	0	-	2	(95.28480102941525 0.00015391502653303813)	`(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	216	7
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	4	2

Confusion

	Predicted +	Predicted -
+	215	4
-	2	35

Precision

0.9907834101382489

Recall

0.9817351598173516

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	215	3	1
-	2	4	31

Precision?

0.9732142857142857

Recall?

0.9954337899543378

Freqs

test

number	freq
0	39
1	214
2	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms	168×	1	valid
16.0ms	340×	0	valid
15.0ms	4×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-tan: 24.0ms (71.4% of total)

adjust: 4.0ms (11.9% of total)

ival-add: 3.0ms (8.9% of total)

ival-sub: 3.0ms (8.9% of total)

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

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

preprocess26.0ms (0.2%)

Memory

-3.8MiB live, 33.4MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0%)

Memory

10.1MiB live, 10.1MiB 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)

localize31.0ms (0.2%)

Memory

6.1MiB live, 43.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.2653669674015681	(tan.f64 (+.f64 x eps))
accuracy	23.4604888811211	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

11.0ms	170×	0	valid
8.0ms	84×	1	valid
5.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-tan: 9.0ms (64.1% of total)

adjust: 2.0ms (14.2% of total)

ival-add: 2.0ms (14.2% of total)

ival-sub: 1.0ms (7.1% of total)

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

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

series18.0ms (0.1%)

Memory

-23.3MiB live, 15.0MiB 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
9.0ms	eps	@	inf	(- (tan (+ x eps)) (tan x))
2.0ms	eps	@	0	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	0	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	-inf	(- (tan (+ x eps)) (tan x))

simplify235.0ms (1.5%)

Memory

51.0MiB live, 314.4MiB 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))

rewrite267.0ms (1.7%)

Memory

-10.9MiB live, 319.1MiB 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))

eval44.0ms (0.3%)

Memory: -18.7MiB live, 64.8MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune64.0ms (0.4%)

Memory

-3.9MiB live, 115.5MiB 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

99.9%

Counts

337 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.8%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
▶	40.3%	(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)))))
	62.9%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
▶	62.9%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.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))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	39.2%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	62.9%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	62.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
	41.0%	(-.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	63.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.9%	(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
▶	62.8%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	62.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
▶	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
	61.1%	(-.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)))))
	62.0%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
	97.2%	#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))))
	98.8%	#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))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (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))
	98.4%	#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))
	96.4%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 1 135 to 514 computations (54.7% saved)

simplify234.0ms (1.5%)

Memory

16.3MiB live, 243.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(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)))))
cost-diff	0	(sin.f64 (-.f64 (+.f64 x eps) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps)))
cost-diff	384	(-.f64 (+.f64 x eps) x)
cost-diff	384	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
cost-diff	0	(/.f64 (sin.f64 x) (cos.f64 x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
cost-diff	0	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
cost-diff	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)))
cost-diff	39808	(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)))
cost-diff	79744	(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)))

Rules

13 450×	`lower-fma.f32`
13 432×	`lower-fma.f64`
4 132×	`lower-+.f32`
4 122×	`lower-+.f64`
3 294×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	1269
0	111	1265
1	210	1089
2	539	940
3	1763	890
0	8231	863

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

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

localize308.0ms (2%)

Memory

8.7MiB live, 364.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.265625	(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
accuracy	0.37337875976844204	(/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
accuracy	23.242365646041893	(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)))))
accuracy	25.662750024385062	(/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
accuracy	0.01953125	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps)))
accuracy	0.0234375	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	23.7351045135628	(-.f64 (+.f64 x eps) x)
accuracy	0	(cos.f64 x)
accuracy	0.01953125	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.2653669674015681	(tan.f64 (+.f64 x eps))
accuracy	23.4604888811211	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.2653669674015681	(tan.f64 (+.f64 x eps))
accuracy	0.3359375	(*.f64 x #s(literal 1/3 binary64))
accuracy	1.8816294667338398	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
accuracy	23.4604888811211	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
accuracy	0.21484375	(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))))
accuracy	0.33984375	(*.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)))
accuracy	0.4979674575565109	#s(approx (- (tan (+ x eps)) (tan x)) (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))
accuracy	0.9772262695368841	(+.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

110.0ms	77×	1	valid
94.0ms	174×	0	valid
14.0ms	4×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 1 150 to 63 computations (94.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-add: 38.0ms (23.5% of total)

ival-mult: 21.0ms (13% of total)

ival-div: 18.0ms (11.1% of total)

ival-sub: 18.0ms (11.1% of total)

adjust: 12.0ms (7.4% of total)

const: 11.0ms (6.8% of total)

ival-pow: 11.0ms (6.8% of total)

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

ival-pow2: 10.0ms (6.2% of total)

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

ival-cos: 5.0ms (3.1% 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)

series144.0ms (0.9%)

Memory

-13.1MiB live, 181.6MiB allocated

Counts

24 → 492

Calls

Call 1

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

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

Calls

123 calls:

Time	Variable		Point	Expression
19.0ms	x	@	inf	(+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))
11.0ms	x	@	0	(+ (* (tan (+ x eps)) (/ (tan (+ x eps)) (+ (tan (+ x eps)) (tan x)))) (neg (/ (pow (tan x) 2) (+ (tan (+ x eps)) (tan x)))))
7.0ms	eps	@	0	(+ (* (tan (+ x eps)) (/ (tan (+ x eps)) (+ (tan (+ x eps)) (tan x)))) (neg (/ (pow (tan x) 2) (+ (tan (+ x eps)) (tan x)))))
6.0ms	x	@	-inf	(+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))
5.0ms	eps	@	0	(+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))

simplify371.0ms (2.4%)

Memory

18.0MiB live, 439.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 040×	`lower-fma.f64`
9 040×	`lower-fma.f32`
6 968×	`lower-*.f64`
6 968×	`lower-*.f32`
6 308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	916	17861
1	2946	17164
0	8808	16712

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 459

Calls

Call 1

Inputs
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -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))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -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))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -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))))) eps)))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 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 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* 1/3 eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
-1/2
(- (* -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)))
(/ (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
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(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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1
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1/2
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 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 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 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))))) eps)))))
(* 1/3 (pow eps 2))
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(* 1/3 x)
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(* 1/3 x)
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1
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(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))))
(* 1/2 (/ (sin x) (cos x)))
(+ (* -1/4 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* 1/2 (/ (sin x) (cos x))))
(+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1 (* eps (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* 1/4 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (* (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1/4 (+ 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))))))) (* -1/8 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* 1/4 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/ (sin eps) (cos eps))
(+ (* x (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 2 (/ (* 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 (- (+ 2 (* x (- (* 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 x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+ (/ (sin 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)))))
(* 2 (/ (sin x) (cos x)))
(+ (* 2 (/ (sin x) (cos x))) (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* 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))))))
(+ (* 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 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)))))

Outputs
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 #s(literal 1/3 binary64) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/3 binary64) (+.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 (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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 #s(literal 1/3 binary64) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/3 binary64) (+.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 (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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 #s(literal 1/3 binary64) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/3 binary64) (+.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 (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 (/.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) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (+.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))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 eps (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) eps))) (/.f64 #s(literal 1/3 binary64) 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) #s(literal 1/3 binary64)))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 eps (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) eps))) (/.f64 #s(literal 1/3 binary64) 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) #s(literal 1/3 binary64)))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 eps (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.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)))) (cos.f64 x)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) eps))) (/.f64 #s(literal 1/3 binary64) 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) #s(literal 1/3 binary64)))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 2) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
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(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))
(fma.f64 x (fma.f64 #s(literal 2/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 #s(literal 1/3 binary64) eps))
(+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))
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x
(* x (+ 1 (/ eps x)))
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(* x (+ 1 (/ eps x)))
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x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(+ eps x)
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(* eps (+ 1 (/ x eps)))
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(* eps (+ 1 (/ x eps)))
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eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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(/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (* -1/4 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* 1/2 (/ (sin x) (cos x))))
(fma.f64 (.f64 #s(literal -1/4 binary64) eps) (+.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 1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1 (* eps (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* 1/4 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.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)) #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (sin.f64 x))) (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (* (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1/4 (+ 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))))))) (* -1/8 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (+ (* -1/8 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 1/4 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* 1/4 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(fma.f64 eps (fma.f64 eps (neg.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 (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))))) (fma.f64 (/.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)) #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (sin.f64 x)))) (sin.f64 x)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #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))))) #s(literal -1/4 binary64) #s(literal -1/24 binary64)))) (fma.f64 (/.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)) #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (sin.f64 x))))) (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (+.f64 #s(literal 2 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 (- (+ 2 (/ (* 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 x (sin.f64 eps)) (/.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)))) (cos.f64 eps)) (+.f64 #s(literal 2 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 (- (+ 2 (* x (- (* 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 #s(literal 1/6 binary64) (fma.f64 (neg.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))) (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 (.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 #s(literal 2 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 x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(* 2 (/ (sin x) (cos x)))
(/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (* 2 (/ (sin x) (cos x))) (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(fma.f64 eps (+.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 2 binary64) (sin.f64 x)) (cos.f64 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))))))
(fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) (/.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)))) (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 (.f64 #s(literal 2 binary64) (sin.f64 x)) (cos.f64 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))))))
(fma.f64 eps (+.f64 (fma.f64 eps (fma.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #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)))))) (neg.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))) #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 2 binary64) (sin.f64 x)) (cos.f64 x)))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))

rewrite521.0ms (3.4%)

Memory

28.0MiB live, 300.2MiB allocated

Rules

5 220×	`lower-fma.f32`
5 202×	`lower-fma.f64`
5 154×	`lower-*.f32`
5 148×	`lower-*.f64`
2 446×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	818
0	111	767
1	510	556
2	4991	556
0	8107	526

Stop Event

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

Counts

24 → 780

Calls

Call 1

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

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

eval598.0ms (3.9%)

Memory: 29.4MiB live, 533.4MiB allocated
Compiler: Compiled 163 668 to 5 662 computations (96.5% saved)

prune327.0ms (2.1%)

Memory

-21.4MiB live, 551.4MiB allocated

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	2 128	17	2 145
Fresh	12	4	16
Picked	5	0	5
Done	0	1	1
Total	2 145	22	2 167

Accuracy

99.9%

Counts

2 167 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(/.f64 (/.f64 (sin.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	99.6%	(/.f64 (/.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
	99.4%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	99.3%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.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))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	90.0%	(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))) (cos.f64 x))
	99.2%	(/.f64 #s(approx (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (.f64 (sin.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (-.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (neg.f64 (cos.f64 x)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (-.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 x))))) (cos.f64 x))
▶	62.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x)))) (cos.f64 x)))
	41.0%	(-.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	63.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	62.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.6%	(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
▶	99.6%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.6%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	98.3%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.8%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (tan.f64 x) (.f64 #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 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	96.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps (fma.f64 (.f64 x (.f64 eps eps)) #s(literal 2/3 binary64) x)))) eps))
▶	96.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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))

Compiler

Compiled 1 209 to 566 computations (53.2% saved)

simplify276.0ms (1.8%)

Memory

20.6MiB live, 340.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	192	(*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))
cost-diff	384	(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))) (cos.f64 x))
cost-diff	12928	(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64)))
cost-diff	192	(-.f64 x x)
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	320	(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x))
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
cost-diff	0	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
cost-diff	0	(sin.f64 (+.f64 eps (-.f64 x x)))
cost-diff	192	(-.f64 x x)
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	320	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))

Rules

15 540×	`lower-fma.f32`
15 538×	`lower-fma.f64`
4 016×	`lower-*.f32`
4 006×	`lower-*.f64`
3 512×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	745
0	101	715
1	187	588
2	467	496
3	2055	496
4	6388	496
0	8262	481

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (1.5%)

Memory

-6.6MiB live, 269.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))) (cos.f64 x))
accuracy	0.01953125	(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))
accuracy	0.14411157620868656	(cos.f64 (+.f64 eps x))
accuracy	5.564210315798858	(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64)))
accuracy	0.0078125	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
accuracy	0.015625	(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
accuracy	0.025722509768442016	(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	0.14411157620868656	(cos.f64 (+.f64 eps x))
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
accuracy	0.180941083102404	(tan.f64 (+.f64 x eps))
accuracy	23.324761886520417	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
accuracy	0	(*.f64 eps eps)
accuracy	0.13556433636143683	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
accuracy	0.23046875	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	31.84764088595802	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
accuracy	0.015625	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
accuracy	0.0234375	(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
accuracy	0.03125	(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
accuracy	0.14411157620868656	(cos.f64 (+.f64 eps x))

Samples

101.0ms	204×	0	valid
48.0ms	47×	1	valid
7.0ms	2×	3	valid
2.0ms	3×	0	invalid

Compiler

Compiled 575 to 67 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-mult: 22.0ms (17.3% of total)

ival-div: 21.0ms (16.5% of total)

ival-add: 19.0ms (14.9% of total)

ival-pow: 15.0ms (11.8% of total)

const: 10.0ms (7.8% of total)

ival-tan: 8.0ms (6.3% of total)

adjust: 7.0ms (5.5% of total)

ival-sin: 5.0ms (3.9% of total)

ival-pow2: 5.0ms (3.9% of total)

ival-sub: 4.0ms (3.1% of total)

ival-cos: 4.0ms (3.1% of total)

ival-log: 4.0ms (3.1% of total)

ival-exp: 3.0ms (2.4% of total)

exact: 1.0ms (0.8% of total)

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

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

series190.0ms (1.2%)

Memory

20.1MiB live, 174.2MiB allocated

Counts

23 → 516

Calls

Call 1

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

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

Calls

129 calls:

Time	Variable		Point	Expression
45.0ms	x	@	inf	(* (log (/ (cos (+ eps x)) (sin (+ eps (- x x))))) -1)
43.0ms	eps	@	inf	(* (log (/ (cos (+ eps x)) (sin (+ eps (- x x))))) -1)
27.0ms	x	@	-inf	(* (log (/ (cos (+ eps x)) (sin (+ eps (- x x))))) -1)
17.0ms	eps	@	-inf	(* (log (/ (cos (+ eps x)) (sin (+ eps (- x x))))) -1)
8.0ms	eps	@	-inf	(/ 1 (- (tan (+ x eps)) (tan x)))

simplify318.0ms (2.1%)

Memory

-6.2MiB live, 307.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 092×	`lower-fma.f64`
10 092×	`lower-fma.f32`
6 818×	`lower-*.f64`
6 818×	`lower-*.f32`
5 492×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	771	12322
1	2487	11899
0	8321	11550

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 491

Calls

Call 1

Inputs
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
0
0
0
0
0
0
0
0
0
0
0
0
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(/ (sin eps) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -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 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (sin x) 2) (pow (cos x) 2))
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(* 1/3 (pow eps 2))
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(* 1/3 (pow eps 2))
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(+ (* -1 (+ (log (cos x)) (* -1 (log eps)))) (/ (* eps (sin x)) (cos x)))
(+ (* -1 (+ (log (cos x)) (* -1 (log eps)))) (* eps (+ (* -1/2 (* eps (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 2 (/ (- (* -1/2 (cos x)) (* -1/6 (cos x))) (cos x)))))) (/ (sin x) (cos x)))))
(+ (* -1 (+ (log (cos x)) (* -1 (log eps)))) (* eps (+ (* eps (+ (* -1/2 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 2 (/ (- (* -1/2 (cos x)) (* -1/6 (cos x))) (cos x))))) (* -1/6 (* eps (+ (* -2 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 6 (/ (* (sin x) (- (* -1/2 (cos x)) (* -1/6 (cos x)))) (pow (cos x) 2)))))))) (/ (sin x) (cos x)))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))))
(* -1 (log (/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))))
(* -1 (log (/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))))
(* -1 (log (/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))))
(* -1 (log (/ (cos eps) (sin eps))))
(+ (* -1 (log (/ (cos eps) (sin eps)))) (/ (* x (sin eps)) (cos eps)))
(+ (* -1 (log (/ (cos eps) (sin eps)))) (* x (+ (* -1/2 (* x (- (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) 1))) (/ (sin eps) (cos eps)))))
(+ (* -1 (log (/ (cos eps) (sin eps)))) (* x (+ (* x (+ (* -1/2 (- (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) 1)) (* -1/6 (* x (+ (* -3 (/ (sin eps) (cos eps))) (+ (* -2 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (/ (sin eps) (cos eps)))))))) (/ (sin eps) (cos eps)))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (+ eps x)) (sin eps))))
(* -1 (log (/ (cos (- eps (* -1 x))) (sin eps))))
(* -1 (log (/ (cos (- eps (* -1 x))) (sin eps))))
(* -1 (log (/ (cos (- eps (* -1 x))) (sin eps))))
(* -1 (log (/ (cos (- eps (* -1 x))) (sin eps))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (sin eps) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 2)))))))) (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (pow (cos x) 2))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ (cos x) eps)
(/ (+ (cos x) (* -1 (* eps (sin x)))) eps)
(/ (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (- (* -1/2 (cos x)) (* -1/6 (cos x))))))) eps)
(/ (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (- (+ (* -1/2 (cos x)) (* (pow eps 2) (- (* 1/24 (cos x)) (+ (* -1/6 (- (* -1/2 (cos x)) (* -1/6 (cos x)))) (* 1/120 (cos x)))))) (* -1/6 (cos x))))))) eps)
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1/2 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1/2 (/ (cos eps) (sin eps))) (* 1/6 x))) 1)) (/ (cos eps) (sin eps)))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (+ eps x)) (sin eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/ (cos (- eps (* -1 x))) (sin eps))

Outputs
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 eps (/.f64 (*.f64 eps (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps eps) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (fma.f64 eps (-.f64 (fma.f64 (-.f64 (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (neg.f64 eps) (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps eps) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (neg.f64 (fma.f64 x (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 2/3 binary64) (/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 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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(-.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)))
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(-.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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(-.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)) (/.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)))))
(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)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.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)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/3 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (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)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.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)
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 4) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
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(* 1/3 (pow eps 2))
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(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 (neg.f64 eps)) (+.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(/ 1 (cos (+ eps x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (+ eps x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (+ eps x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (+ eps x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (+ (cos x) (* -1 (* eps (sin x)))) eps)
(/.f64 (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))) eps)
(/ (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (- (* -1/2 (cos x)) (* -1/6 (cos x))))))) eps)
(/.f64 (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/3 binary64))) (sin.f64 x)) (cos.f64 x)) eps)
(/ (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (- (+ (* -1/2 (cos x)) (* (pow eps 2) (- (* 1/24 (cos x)) (+ (* -1/6 (- (* -1/2 (cos x)) (* -1/6 (cos x)))) (* 1/120 (cos x)))))) (* -1/6 (cos x))))))) eps)
(/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps eps) (-.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (fma.f64 (cos.f64 x) #s(literal 1/120 binary64) (.f64 (cos.f64 x) #s(literal 1/18 binary64)))) (.f64 (cos.f64 x) #s(literal -1/3 binary64))) (neg.f64 (sin.f64 x))) (cos.f64 x)) eps)
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- x (* -1 eps))) (sin (neg (* -1 eps))))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos eps) (sin eps))
(/.f64 (cos.f64 eps) (sin.f64 eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(-.f64 (/.f64 (cos.f64 eps) (sin.f64 eps)) x)
(+ (* x (- (* -1/2 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(fma.f64 x (fma.f64 (/.f64 (cos.f64 eps) (sin.f64 eps)) (*.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)) (/.f64 (cos.f64 eps) (sin.f64 eps)))
(+ (* x (- (* x (+ (* -1/2 (/ (cos eps) (sin eps))) (* 1/6 x))) 1)) (/ (cos eps) (sin eps)))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 eps) (sin.f64 eps)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (/.f64 (cos.f64 eps) (sin.f64 eps)))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (+ eps x)) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))
(/ (cos (- eps (* -1 x))) (sin eps))
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 eps))

rewrite73.0ms (0.5%)

Memory

-12.3MiB live, 62.6MiB allocated

Rules

220×	`lower-*.f32`
210×	`lower-*.f64`
192×	`lower-/.f32`
178×	`lower-/.f64`
150×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	663
0	101	624
0	498	600

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

23 → 101

Calls

Call 1

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

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

eval90.0ms (0.6%)

Memory: 27.6MiB live, 141.7MiB allocated
Compiler: Compiled 18 537 to 1 059 computations (94.3% saved)

prune484.0ms (3.2%)

Memory

-5.5MiB live, 398.0MiB allocated

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	717	15	732
Fresh	6	10	16
Picked	3	2	5
Done	0	1	1
Total	726	28	754

Accuracy

100.0%

Counts

754 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(/.f64 (/.f64 (sin.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
▶	99.3%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	90.0%	(/.f64 (exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))) #s(literal -1 binary64))) (cos.f64 x))
✓	62.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x)))) (cos.f64 x)))
	41.0%	(-.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	63.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	62.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.9%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (cos.f64 x)))
	99.2%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)))) (cos.f64 x)))
▶	99.6%	(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
▶	99.9%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))
	99.4%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64))) (neg.f64 (sin.f64 x))) (cos.f64 x))))))
▶	99.2%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
	98.9%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))))))
	99.5%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) #s(approx ( (cos x) (cos (+ eps x))) (fma.f64 eps (-.f64 (.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (.f64 (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (*.f64 (cos.f64 x) (sin.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	99.4%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.3%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
	99.3%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.6%	(.f64 #s(approx (sin (+ eps (- x x))) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.6%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	98.3%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.8%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
▶	96.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
✓	96.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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))
	54.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)))

Compiler

Compiled 1 260 to 707 computations (43.9% saved)

simplify240.0ms (1.6%)

Memory

26.5MiB live, 294.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	192	(-.f64 x x)
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	320	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
cost-diff	6080	(fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))
cost-diff	192	(-.f64 x x)
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	256	(-.f64 x (+.f64 eps x))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)
cost-diff	0	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps))
cost-diff	0	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps)))
cost-diff	384	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64)))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
cost-diff	640	(fma.f64 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))
cost-diff	0	(sin.f64 (+.f64 eps (-.f64 x x)))
cost-diff	192	(-.f64 x x)
cost-diff	192	(+.f64 eps (-.f64 x x))
cost-diff	320	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))

Rules

9 482×	`lower-fma.f32`
9 472×	`lower-fma.f64`
3 868×	`lower-*.f32`
3 840×	`lower-*.f64`
3 614×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	1001
0	146	975
1	286	833
2	682	734
3	3038	730
4	6589	730
0	8268	697

Stop Event

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

Calls

Call 1

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

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

localize456.0ms (3%)

Memory

-53.8MiB live, 380.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x))
accuracy	0.03515625	(/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)))))
accuracy	0.03515625	(.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))
accuracy	0.4853436142345075	#s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)))
accuracy	0.05126609887433277	(+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x))))
accuracy	0.20428058872095545	(cos.f64 (+.f64 x (+.f64 eps x)))
accuracy	0.26171875	(+.f64 x (+.f64 eps x))
accuracy	23.7351045135628	(-.f64 x (+.f64 eps x))
accuracy	0.0234375	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	0.23828125	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
accuracy	0.3056191418837318	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps))
accuracy	0.23828125	(.f64 (.f64 eps eps) #s(literal 2/3 binary64))
accuracy	0.34765625	(*.f64 eps #s(literal 1/3 binary64))
accuracy	0.4979674575565109	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
accuracy	33.325843070972155	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64)))))
accuracy	0.01953125	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))
accuracy	0.02734375	(*.f64 (sin.f64 eps) (sin.f64 x))
accuracy	0.03515625	(/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))
accuracy	0.03515625	(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))

Samples

157.0ms	84×	1	valid
108.0ms	167×	0	valid
9.0ms	3×	3	valid
4.0ms	2×	2	valid

Compiler

Compiled 723 to 93 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

adjust: 67.0ms (28.3% of total)

ival-mult: 45.0ms (19% of total)

ival-add: 34.0ms (14.4% of total)

ival-div: 23.0ms (9.7% of total)

ival-cos: 13.0ms (5.5% of total)

const: 13.0ms (5.5% of total)

ival-sub: 11.0ms (4.6% of total)

ival-pow: 10.0ms (4.2% of total)

ival-sin: 10.0ms (4.2% of total)

ival-pow2: 6.0ms (2.5% of total)

ival-tan: 4.0ms (1.7% of total)

exact: 1.0ms (0.4% of total)

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

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

series73.0ms (0.5%)

Memory

20.4MiB live, 129.1MiB allocated

Counts

30 → 660

Calls

Call 1

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

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

Calls

165 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)
2.0ms	eps	@	-inf	(* (sin (+ eps (- x x))) (/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))
2.0ms	x	@	inf	(* (sin (+ eps (- x x))) (/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))
1.0ms	eps	@	inf	(* (sin (+ eps (- x x))) (/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))
1.0ms	x	@	-inf	(* (sin (+ eps (- x x))) (/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))

simplify400.0ms (2.6%)

Memory

-18.6MiB live, 457.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 746×	`lower-fma.f64`
10 746×	`lower-fma.f32`
7 336×	`lower-*.f64`
7 336×	`lower-*.f32`
5 568×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	862	11750
1	2761	11460
0	8506	11016

Stop Event

1×	iter limit
1×	node limit

Counts

660 → 630

Calls

Call 1

Inputs
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ (sin eps) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
0
0
0
0
0
0
0
0
0
0
0
0
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* eps x)
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* 2/3 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (- (* -2/3 x) (* 1/3 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(* eps (* x (+ 1 (* 2/3 (pow eps 2)))))
(* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))
(* -1 (* eps (* x (- (* -2/3 (pow eps 2)) 1))))
(* -1 (* x (+ (* -1/3 (/ (pow eps 2) x)) (* eps (- (* -2/3 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/3 (/ (pow eps 2) x)) (* eps (- (* -2/3 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/3 (/ (pow eps 2) x)) (* eps (- (* -2/3 (pow eps 2)) 1)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -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))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -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 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -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))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 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 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 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))))) eps)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
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eps
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(sin (neg (* -1 eps)))
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(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (sin eps) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 2)))))))) (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (pow (cos x) 2))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(/ 1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(cos eps)
(+ (cos eps) (* -2 (* x (sin eps))))
(+ (cos eps) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
(+ (cos eps) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (* 2 x))
(+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* -1/2 (* eps (cos (* 2 x)))) (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x)))))) (sin (* 2 x)))))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(+ (cos eps) (cos (neg eps)))
(+ (cos eps) (+ (cos (neg eps)) (* -2 (* x (sin eps)))))
(+ (cos eps) (+ (cos (neg eps)) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps))))))
(+ (cos eps) (+ (cos (neg eps)) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps))))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (- eps (* -2 x))))
(+ (cos (neg eps)) (cos (- eps (* -2 x))))
(+ (cos (neg eps)) (cos (- eps (* -2 x))))
(+ (cos (neg eps)) (cos (- eps (* -2 x))))
(+ 1 (cos (* 2 x)))
(+ 1 (+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (* -1/2 (cos (* 2 x))) 1/2)) (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x))))) 1/2)) (sin (* 2 x))))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (neg eps)) (cos (+ eps (* 2 x))))
(+ (cos (* -1 eps)) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (* -1 eps)) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (* -1 eps)) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (* -1 eps)) (cos (- (* 2 x) (* -1 eps))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (sin eps) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 2)))))))) (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (pow (cos x) 2))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))

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

rewrite70.0ms (0.5%)

Memory

18.4MiB live, 108.8MiB allocated

Rules

338×	`lower-*.f32`
312×	`lower-*.f64`
238×	`lower-/.f32`
238×	`lower-+.f32`
228×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	845
0	144	791
0	712	767

Stop Event

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

Counts

30 → 130

Calls

Call 1

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

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

eval108.0ms (0.7%)

Memory: 9.7MiB live, 198.7MiB allocated
Compiler: Compiled 23 689 to 1 390 computations (94.1% saved)

prune465.0ms (3%)

Memory

5.4MiB live, 682.4MiB allocated

Pruning

38 alts after pruning (34 fresh and 4 done)

	Pruned	Kept	Total
New	837	21	858
Fresh	7	13	20
Picked	4	1	5
Done	0	3	3
Total	848	38	886

Accuracy

100.0%

Counts

886 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(/.f64 (/.f64 (sin.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	99.5%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
✓	99.3%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	98.9%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))) (cos.f64 x))
	53.0%	(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* (* eps eps) -1/6)) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/6 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	90.0%	(/.f64 (exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))) #s(literal -1 binary64))) (cos.f64 x))
	99.3%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
✓	62.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
	41.0%	(-.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	63.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	62.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	40.1%	(.f64 (sin.f64 (/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
	62.9%	(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
	99.4%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (fma.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) #s(literal 2 binary64))))
	98.9%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) (+.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 eps) (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal 2 binary64))))
	99.6%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64))))
	99.6%	(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 x #s(literal 2 binary64) eps))))))
	98.3%	(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))
	99.4%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.3%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
	99.7%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
	99.3%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
	99.5%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))
	99.2%	(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
	99.6%	(.f64 #s(approx (sin (+ eps (- x x))) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
	99.6%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	98.3%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.8%	#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) 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 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
✓	96.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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))
	96.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (.f64 eps (fma.f64 eps (fma.f64 (.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64)) x)))) eps))
	96.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x)))) eps))
	96.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
	54.4%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64))))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) eps)))
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Compiler

Compiled 2 859 to 889 computations (68.9% saved)

regimes65.0ms (0.4%)

Memory

-4.7MiB live, 79.3MiB allocated

Counts

75 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

23.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
19.0ms	eps
18.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes84.0ms (0.5%)

Memory

-4.9MiB live, 70.2MiB allocated

Counts

62 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (.f64 eps (fma.f64 eps (fma.f64 (.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64)) x)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 17/9 binary64) #s(literal 4/3 binary64)) (.f64 x (.f64 eps eps)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 #s(literal 2/3 binary64) eps) eps))) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64))))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* (* eps eps) -1/6)) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/6 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(.f64 #s(approx (sin (+ eps (- x x))) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(/.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)))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 x #s(literal 2 binary64) eps))))))
(/.f64 (/.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x)))) (cos.f64 x)))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))) (cos.f64 x))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) (+.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 eps) (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal 2 binary64))))
(/.f64 (/.f64 (sin.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 (sin.f64 (/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (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)))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))))))
(/.f64 (exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))) #s(literal -1 binary64))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))) (cos.f64 x))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)))) (cos.f64 x)))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (fma.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) #s(literal 2 binary64))))

Outputs

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

Calls

3 calls:

49.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
17.0ms	x
15.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes57.0ms (0.4%)

Memory

-19.2MiB live, 66.1MiB allocated

Counts

60 → 1

Calls

Call 1

Inputs
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 17/9 binary64) #s(literal 4/3 binary64)) (.f64 x (.f64 eps eps)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 #s(literal 2/3 binary64) eps) eps))) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3 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)))
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(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* (* eps eps) -1/6)) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/6 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
(.f64 #s(approx (sin (+ eps (- x x))) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(/.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)))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 x #s(literal 2 binary64) eps))))))
(/.f64 (/.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x)))) (cos.f64 x)))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))) (cos.f64 x))
(*.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) (+.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 eps) (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal 2 binary64))))
(/.f64 (/.f64 (sin.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) x)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 (sin.f64 (/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (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)))
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(/.f64 (exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))) #s(literal -1 binary64))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps (-.f64 x x))))) #s(literal -1 binary64))) (cos.f64 x))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (cos (+ eps x)) (fma.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)))) (cos.f64 x)))

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

Calls

3 calls:

20.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	x
15.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

8.8MiB live, 44.6MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (.f64 eps (fma.f64 eps (fma.f64 (.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64)) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps (fma.f64 (.f64 x (.f64 eps eps)) #s(literal 2/3 binary64) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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)) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 17/9 binary64) #s(literal 4/3 binary64)) (.f64 x (.f64 eps eps)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 #s(literal 2/3 binary64) eps) eps))) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64))))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* (* eps eps) -1/6)) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/6 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))

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

Calls

3 calls:

13.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

4.1MiB live, 40.9MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (.f64 eps (fma.f64 eps (fma.f64 (.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64)) x)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 eps (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64))) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 2/3 binary64)) (.f64 eps eps) eps)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 17/9 binary64) #s(literal 4/3 binary64)) (.f64 x (.f64 eps eps)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 #s(literal 2/3 binary64) eps) eps))) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) (.f64 eps #s(approx (+ ( eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64))))))) (.f64 eps eps)) (-.f64 (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (+.f64 (fma.f64 x (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) x) (.f64 eps #s(literal 1/3 binary64)))))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (/ (sin (- (+ x eps) x)) (cos (+ x eps))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(.f64 (sin.f64 (+.f64 eps (-.f64 x x))) #s(approx (/ 1 (/ (+ (cos (+ x (+ eps x))) (cos (- x (+ eps x)))) 2)) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* (* eps eps) -1/6)) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/6 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(.f64 #s(approx (sin (+ eps (- x x))) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 eps x))) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))

Outputs

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

Calls

3 calls:

9.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	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)

regimes25.0ms (0.2%)

Memory

-1.5MiB live, 46.4MiB allocated

Counts

23 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

0.6MiB live, 37.8MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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)

regimes18.0ms (0.1%)

Memory

-9.1MiB live, 28.8MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	x
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	eps

Results

Accuracy	Segments	Branch
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)

regimes8.0ms (0.1%)

Memory

17.6MiB live, 17.7MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.5%	1	`eps`
96.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
96.5%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

10.6MiB live, 10.6MiB 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)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (/ (sin x) (cos x))))) (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (* x (* (* eps eps) 2/3)) x)) (* eps (* eps 1/3))) (*.f64 eps x))) eps))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.3%	1	`x`
96.3%	1	`eps`
96.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify14.0ms (0.1%)

Memory

-13.8MiB live, 23.8MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	734
1	164	734
2	174	734
3	180	734
4	183	734

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (8.4%)

Memory

17.1MiB live, 967.8MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
10 746×	`lower-fma.f64`
10 746×	`lower-fma.f32`
10 092×	`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	771	12322
1	2487	11899
0	8321	11550
0	72	663
0	101	624
0	498	600
0	58	818
0	111	767
1	510	556
2	4991	556
0	8107	526
0	93	845
0	144	791
0	712	767
0	916	17861
1	2946	17164
0	8808	16712
0	862	11750
1	2761	11460
0	8506	11016
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16

Stop Event

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

Compiler

Compiled 602 to 303 computations (49.7% saved)

preprocess198.0ms (1.3%)

Memory: -20.3MiB live, 191.6MiB allocated
Compiler: Compiled 440 to 162 computations (63.2% 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%)

analyze71.0ms (0.5%)

sample6.6s (43.3%)

explain120.0ms (0.8%)

preprocess26.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize31.0ms (0.2%)

series18.0ms (0.1%)

simplify235.0ms (1.5%)

rewrite267.0ms (1.7%)

eval44.0ms (0.3%)

prune64.0ms (0.4%)

simplify234.0ms (1.5%)

localize308.0ms (2%)

series144.0ms (0.9%)

simplify371.0ms (2.4%)

rewrite521.0ms (3.4%)

eval598.0ms (3.9%)

prune327.0ms (2.1%)

simplify276.0ms (1.8%)

localize235.0ms (1.5%)

series190.0ms (1.2%)

simplify318.0ms (2.1%)

rewrite73.0ms (0.5%)

eval90.0ms (0.6%)

prune484.0ms (3.2%)

simplify240.0ms (1.6%)

localize456.0ms (3%)

series73.0ms (0.5%)

simplify400.0ms (2.6%)

rewrite70.0ms (0.5%)

eval108.0ms (0.7%)

prune465.0ms (3%)

regimes65.0ms (0.4%)

regimes84.0ms (0.5%)

regimes57.0ms (0.4%)

regimes31.0ms (0.2%)

regimes27.0ms (0.2%)

regimes25.0ms (0.2%)

regimes21.0ms (0.1%)

regimes18.0ms (0.1%)

regimes8.0ms (0.1%)

regimes4.0ms (0%)

simplify14.0ms (0.1%)

soundness1.3s (8.4%)

preprocess198.0ms (1.3%)

end0.0ms (0%)

Profiling

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

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