Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze55.0ms (0.4%)

Memory

-8.8MiB live, 75.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.4s (47.9%)

Memory

71.0MiB live, 8 396.1MiB allocated

Samples

4.0s	26 007×	0	invalid
931.0ms	5 486×	0	valid
832.0ms	2 770×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 4.2s

const: 800.0ms (18.9% of total)

ival-tan: 718.0ms (17% of total)

ival-sub: 544.0ms (12.8% of total)

ival-<=: 534.0ms (12.6% of total)

ival-add: 468.0ms (11.1% of total)

ival-<: 344.0ms (8.1% of total)

ival-fabs: 264.0ms (6.2% of total)

ival-mult: 249.0ms (5.9% of total)

adjust: 154.0ms (3.6% of total)

ival-and: 101.0ms (2.4% of total)

exact: 46.0ms (1.1% of total)

ival-assert: 14.0ms (0.3% of total)

Bogosity

explain92.0ms (0.6%)

Memory

32.1MiB live, 70.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
231	2	(-2.0551155756050403e-128 1.3249092854559037e-130)	3	(1.1885620577001862e-305 2.916540752734288e-307)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
1	0	-	0	-	`(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	230	7
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	228	4
-	2	22

Precision

0.991304347826087

Recall

0.9827586206896551

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	228	4	0
-	2	3	19

Precision?

0.9789029535864979

Recall?

1.0

Freqs

test

number	freq
0	26
1	229
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	176×	1	valid
16.0ms	336×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-tan: 9.0ms (46.9% of total)

adjust: 4.0ms (20.8% of total)

ival-sub: 3.0ms (15.6% of total)

ival-add: 3.0ms (15.6% of total)

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

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

preprocess50.0ms (0.3%)

Memory

-16.2MiB live, 29.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB 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)

localize48.0ms (0.3%)

Memory

-1.7MiB live, 35.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.05182795736094859	(tan.f64 (+.f64 x eps))
accuracy	24.256286789743196	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

31.0ms	88×	1	valid
8.0ms	168×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-tan: 5.0ms (51% of total)

adjust: 2.0ms (20.4% of total)

ival-sub: 2.0ms (20.4% of total)

ival-add: 2.0ms (20.4% of total)

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

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

series35.0ms (0.2%)

Memory

-22.0MiB live, 15.7MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

Time	Variable		Point	Expression
26.0ms	eps	@	0	(- (tan (+ x eps)) (tan x))
2.0ms	eps	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	0	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	-inf	(- (tan (+ x eps)) (tan x))

simplify283.0ms (1.8%)

Memory

27.7MiB live, 336.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite265.0ms (1.7%)

Memory

1.1MiB live, 438.8MiB 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))

eval62.0ms (0.4%)

Memory: -16.9MiB live, 101.4MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune54.0ms (0.3%)

Memory

40.1MiB live, 156.2MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	325	11	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	325	12	337

Accuracy

100.0%

Counts

337 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
	62.1%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	62.0%	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	61.8%	(-.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)))
▶	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
	61.8%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
	99.0%	#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))))
	100.0%	#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))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 567 to 276 computations (51.3% saved)

simplify243.0ms (1.6%)

Memory

-2.3MiB live, 356.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff	320	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
cost-diff	0	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
cost-diff	0	#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))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 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)))
cost-diff	0	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	192	(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64))
cost-diff	5824	(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	26816	(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))

Rules

15 784×	`lower-fma.f32`
15 764×	`lower-fma.f64`
3 440×	`lower-*.f32`
3 432×	`lower-*.f64`
2 848×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	769
0	111	756
1	202	676
2	461	676
3	1209	676
4	4112	676
5	6962	676
0	8005	666

Stop Event

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

Calls

Call 1

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

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

localize322.0ms (2.1%)

Memory

-19.6MiB live, 410.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
accuracy	0.03991862703305532	(cos.f64 (+.f64 x eps))
accuracy	0.04906380013364235	(sin.f64 (+.f64 x eps))
accuracy	24.2497189224685	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
accuracy	0.01171875	(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
accuracy	0.03991862703305532	(cos.f64 (+.f64 x eps))
accuracy	0.04906380013364235	(sin.f64 (+.f64 x eps))
accuracy	24.256286789743196	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
accuracy	0.09375	(.f64 x (.f64 x x))
accuracy	0.11328125	(.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)))
accuracy	0.45869496070077215	#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))
accuracy	24.256286789743196	(-.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)))
accuracy	0.05182795736094859	(tan.f64 (+.f64 x eps))
accuracy	0.31640625	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.6107228549615354	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
accuracy	24.256286789743196	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
accuracy	0.01953125	(-.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))))
accuracy	0.028007519536884032	(pow.f64 (sin.f64 x) #s(literal 4 binary64))
accuracy	0.12109375	(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.9765625	(+.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

136.0ms	164×	0	valid
95.0ms	92×	1	valid

Compiler

Compiled 666 to 63 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 181.0ms

const: 32.0ms (17.6% of total)

ival-mult: 29.0ms (16% of total)

ival-pow2: 29.0ms (16% of total)

ival-div: 21.0ms (11.6% of total)

ival-add: 20.0ms (11% of total)

adjust: 12.0ms (6.6% of total)

ival-sin: 11.0ms (6.1% of total)

ival-pow: 10.0ms (5.5% of total)

ival-tan: 5.0ms (2.8% of total)

ival-cos: 5.0ms (2.8% of total)

ival-sub: 4.0ms (2.2% of total)

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

exact: 1.0ms (0.6% of total)

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

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

series72.0ms (0.5%)

Memory

-2.8MiB live, 75.2MiB allocated

Counts

22 → 420

Calls

Call 1

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

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

Calls

105 calls:

Time	Variable		Point	Expression
13.0ms	eps	@	inf	(+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
7.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
4.0ms	x	@	-inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
3.0ms	x	@	inf	(+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))
2.0ms	eps	@	0	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)

simplify247.0ms (1.6%)

Memory

38.3MiB live, 346.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8 140×	`lower-fma.f64`
8 140×	`lower-fma.f32`
6 118×	`lower-*.f64`
6 118×	`lower-*.f32`
2 984×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	452	9017
1	1386	8701
2	4477	8604
0	8118	8261

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 412

Calls

Call 1

Inputs
-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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1/3
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 4)
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
1/2
(+ 1/2 (* 4/3 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 2/15 x)
(* x (+ 2/15 (* 17/315 (pow x 2))))
(* x (+ 2/15 (* 17/315 (pow x 2))))
(* x (+ 2/15 (* 17/315 (pow x 2))))
(* 17/315 (pow x 3))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* 17/315 (pow x 3))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* -1/3 (pow x 2)) 1/2)
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -2/9 binary64) #s(literal -1/3 binary64))) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -17/135 binary64) #s(literal -2/9 binary64))) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 eps eps)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps)))) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps)))) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(.f64 (.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(.f64 (.f64 eps (*.f64 eps eps)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
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(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (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 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow x 4)
(.f64 (.f64 x x) (*.f64 x x))
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal 1 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5 binary64)) #s(literal -2/3 binary64)) #s(literal 1 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -34/945 binary64) #s(literal 1/5 binary64)) #s(literal -2/3 binary64)) #s(literal 1 binary64)))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 4/3 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/9 binary64) #s(literal 4/3 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 248/135 binary64) #s(literal 17/9 binary64))) #s(literal 4/3 binary64)) #s(literal 1/2 binary64))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(- (+ 1/2 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 2/15 x)
(*.f64 x #s(literal 2/15 binary64))
(* x (+ 2/15 (* 17/315 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))
(* x (+ 2/15 (* 17/315 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))
(* x (+ 2/15 (* 17/315 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))
(* 17/315 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 17/315 binary64))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(* 17/315 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 17/315 binary64))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(* (pow x 3) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (.f64 x x))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

rewrite493.0ms (3.2%)

Memory

-364.8MiB live, 396.4MiB allocated

Rules

5 142×	`lower-fma.f32`
5 122×	`lower-fma.f64`
4 704×	`lower-*.f32`
4 696×	`lower-*.f64`
3 464×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	494
0	111	469
1	495	350
2	4306	340
0	9066	329

Stop Event

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

Counts

22 → 464

Calls

Call 1

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

Outputs
(+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
(+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
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(pow.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 2 binary64)))))
(.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(+.f64 (.f64 x #s(literal 2/15 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 x #s(literal 2/15 binary64)))
(fma.f64 x #s(literal 2/15 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 17/315 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)) (*.f64 x #s(literal 2/15 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 17/315 binary64)) (*.f64 x #s(literal 2/15 binary64)))
(fma.f64 #s(literal 17/315 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 2/15 binary64)))
(fma.f64 #s(literal 2/15 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 17/315 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 17/315 binary64) (*.f64 x #s(literal 2/15 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) x (*.f64 x #s(literal 2/15 binary64)))
(fma.f64 (.f64 x #s(literal 17/315 binary64)) (.f64 x x) (*.f64 x #s(literal 2/15 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/31255875 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 8/3375 binary64))) (fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (-.f64 (.f64 (.f64 x #s(literal 2/15 binary64)) (.f64 x #s(literal 2/15 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (*.f64 x #s(literal 2/15 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 (.f64 x #s(literal 2/15 binary64)) (.f64 x #s(literal 2/15 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 x #s(literal 2/15 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/31255875 binary64)) #s(literal 8/3375 binary64))) (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/99225 binary64) (-.f64 #s(literal 4/225 binary64) (.f64 (*.f64 x x) #s(literal 34/4725 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/99225 binary64) #s(literal -4/225 binary64))) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal -2/15 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/31255875 binary64)) #s(literal 8/3375 binary64)) x) (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/99225 binary64) (-.f64 #s(literal 4/225 binary64) (.f64 (*.f64 x x) #s(literal 34/4725 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 289/99225 binary64) #s(literal -4/225 binary64)) x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal -2/15 binary64)))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 17/315 binary64)) #s(literal 2/15 binary64)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

eval176.0ms (1.1%)

Memory: -33.8MiB live, 337.1MiB allocated
Compiler: Compiled 46 375 to 2 515 computations (94.6% saved)

prune118.0ms (0.8%)

Memory

40.1MiB live, 237.6MiB allocated

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	1 169	7	1 176
Fresh	5	1	6
Picked	3	2	5
Done	0	1	1
Total	1 177	11	1 188

Accuracy

100.0%

Counts

1 188 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.0%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (neg.f64 (tan.f64 x)))
✓	62.0%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
	62.1%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	24.0%	(-.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
✓	62.0%	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.8%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
▶	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))

Compiler

Compiled 387 to 200 computations (48.3% saved)

simplify280.0ms (1.8%)

Memory

8.7MiB live, 314.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
cost-diff	0	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff	0	(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
cost-diff	0	(sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
cost-diff	0	(/.f64 (sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (+.f64 x eps)))
cost-diff	0	(-.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
cost-diff	192	(fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
cost-diff	0	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
cost-diff	18880	(fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Rules

21 740×	`lower-fma.f32`
21 720×	`lower-fma.f64`
4 024×	`lower-*.f32`
4 016×	`lower-*.f64`
2 670×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	1203
0	128	1186
1	232	1060
2	500	1056
3	1290	1038
4	3736	1038
5	6187	1038
0	8136	990

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

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

localize329.0ms (2.1%)

Memory

-0.6MiB live, 352.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.015625	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.1573865416661845	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
accuracy	0.10546875	(fma.f64 eps (-.f64 eps x) (*.f64 x x))
accuracy	0.14453125	(.f64 eps (.f64 eps eps))
accuracy	24.256286789743196	(-.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
accuracy	40.106066111250485	(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
accuracy	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
accuracy	0.140625	(fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
accuracy	0.19921875	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	0.9652715374323312	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
accuracy	0	(*.f64 eps eps)
accuracy	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
accuracy	0.19921875	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	32.049071912971506	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
accuracy	0.01953125	(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))
accuracy	0.024101269536884032	(pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))
accuracy	0.140625	(fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	6.701946408217418	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

128.0ms	91×	1	valid
111.0ms	165×	0	valid

Compiler

Compiled 826 to 72 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 204.0ms

ival-pow: 46.0ms (22.6% of total)

ival-div: 42.0ms (20.6% of total)

ival-mult: 28.0ms (13.7% of total)

ival-add: 24.0ms (11.8% of total)

const: 16.0ms (7.8% of total)

adjust: 14.0ms (6.9% of total)

ival-sub: 7.0ms (3.4% of total)

ival-cos: 7.0ms (3.4% of total)

ival-sin: 7.0ms (3.4% of total)

ival-pow2: 6.0ms (2.9% of total)

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

exact: 1.0ms (0.5% of total)

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

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

series92.0ms (0.6%)

Memory

-2.7MiB live, 80.7MiB allocated

Counts

26 → 528

Calls

Call 1

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

Outputs
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (taylor 0 eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (taylor 0 eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (taylor 0 eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (taylor inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))) (taylor inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))) (taylor inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))) (taylor inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (taylor -inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) (taylor -inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) (taylor -inf eps) (#s(alt (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor -inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor -inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor -inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor -inf x) (#s(alt (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (patch (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (pow x 2)) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* -1 x))) (pow x 2)) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* -1 x))) (pow x 2)) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps))) (taylor inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps))) (taylor inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* -1 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* -1 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps x)))) (taylor inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps x)))) (taylor -inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (fma.f64 eps (-.f64 eps x) (.f64 x x)) (patch (fma.f64 eps (-.f64 eps x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) (taylor 0 x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) (taylor 0 x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

132 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	(+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps)))
3.0ms	x	@	inf	(+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps)))
1.0ms	x	@	0	(+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2)))
1.0ms	eps	@	0	(+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps)
1.0ms	eps	@	0	(+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2)))

simplify282.0ms (1.8%)

Memory

18.6MiB live, 369.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 468×	`lower-fma.f64`
8 468×	`lower-fma.f32`
5 664×	`lower-*.f64`
5 664×	`lower-*.f32`
3 206×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	574	14740
1	1863	14357
2	6213	14030
0	8954	13412

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 520

Calls

Call 1

Inputs
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* 4/3 (* eps x))))))
(* x (+ eps (* x (+ 1 (* x (+ (* 2/3 x) (* 4/3 eps)))))))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))
(/ (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)))))
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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)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
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(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
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(/ (sin eps) (cos eps))
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(/ (sin eps) (cos eps))
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(/ (sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2)))) (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 (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x)))
(/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x)))
(/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x)))
(/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x)))
(/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps))))
(/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps))))
(/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps))))
(/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
(* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))
(/ (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
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(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)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow x 2)
(+ (* -1 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(+ (* eps (+ eps (* -1 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(* (pow eps 2) (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ x (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(+ (* x (+ x (* -1 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1 (/ (pow eps 2) x))) x))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)

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

rewrite295.0ms (1.9%)

Memory

6.4MiB live, 387.3MiB allocated

Rules

6 942×	`lower-fma.f32`
6 922×	`lower-fma.f64`
5 434×	`lower-*.f32`
5 426×	`lower-*.f64`
2 372×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	1106
0	128	1054
1	584	723
2	5543	723
0	8679	678

Stop Event

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

Counts

26 → 459

Calls

Call 1

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

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

eval209.0ms (1.3%)

Memory: -21.6MiB live, 264.6MiB allocated
Compiler: Compiled 36 177 to 2 314 computations (93.6% saved)

prune134.0ms (0.9%)

Memory

18.1MiB live, 225.4MiB allocated

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	1 132	13	1 145
Fresh	3	0	3
Picked	4	1	5
Done	2	1	3
Total	1 141	15	1 156

Accuracy

100.0%

Counts

1 156 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.8%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -2 binary64)) eps eps))
▶	99.8%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	99.2%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	99.2%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
	99.1%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x (.f64 x (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64))))) eps eps))
	98.9%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
▶	100.0%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps #s(approx (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3)) (fma.f64 x (.f64 #s(literal 4/3 binary64) (.f64 x x)) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
✓	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
▶	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
▶	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))))) eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (*.f64 x (+.f64 x eps)))) eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) (.f64 eps #s(literal 4/3 binary64))) #s(literal 1 binary64)) eps)))) eps))
▶	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))) eps))

Compiler

Compiled 483 to 242 computations (49.9% saved)

simplify392.0ms (2.5%)

Memory

-5.4MiB live, 397.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(tan.f64 x)
cost-diff	0	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
cost-diff	0	(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
cost-diff	0	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x)))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))))) eps))
cost-diff	0	#s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps)))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))) eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	12416	(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))

Rules

20 658×	`lower-fma.f32`
20 640×	`lower-fma.f64`
4 180×	`lower-+.f32`
4 178×	`lower-+.f64`
3 744×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1548
0	113	1548
1	243	1380
2	569	1332
3	1403	1308
4	3788	1308
5	7226	1308
0	8502	1248

Stop Event

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

Calls

Call 1

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

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

localize316.0ms (2%)

Memory

19.2MiB live, 407.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(tan.f64 x)
accuracy	0.00390625	(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
accuracy	0.0234375	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy	0.1573865416661845	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
accuracy	0.01171875	(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))
accuracy	0.12109375	(fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x))
accuracy	0.31640625	(*.f64 x #s(literal 4/3 binary64))
accuracy	0.9652715374323312	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x))))
accuracy	0.1953125	(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))
accuracy	0.31640625	(*.f64 x #s(literal 4/3 binary64))
accuracy	0.9652715374323312	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))))
accuracy	32.04877347385958	#s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))))
accuracy	0	(*.f64 x eps)
accuracy	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))) eps))
accuracy	6.701946408217418	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps)))
accuracy	32.887527393646195	#s(approx (+ (* eps (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))
accuracy	0.0234375	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy	0.024101269536884032	(pow.f64 (tan.f64 x) #s(literal 3 binary64))
accuracy	0.140625	(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
accuracy	6.701946408217418	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))

Samples

123.0ms	91×	1	valid
94.0ms	165×	0	valid

Compiler

Compiled 872 to 76 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 188.0ms

ival-mult: 36.0ms (19.2% of total)

ival-add: 28.0ms (14.9% of total)

adjust: 27.0ms (14.4% of total)

ival-pow2: 21.0ms (11.2% of total)

ival-div: 20.0ms (10.7% of total)

ival-pow: 20.0ms (10.7% of total)

const: 13.0ms (6.9% of total)

ival-cos: 9.0ms (4.8% of total)

ival-tan: 5.0ms (2.7% of total)

ival-sin: 5.0ms (2.7% of total)

ival-sub: 4.0ms (2.1% of total)

exact: 1.0ms (0.5% of total)

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

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

series83.0ms (0.5%)

Memory

16.1MiB live, 134.9MiB allocated

Counts

26 → 564

Calls

Call 1

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

Calls

141 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
1.0ms	x	@	-inf	(+ (* eps (+ (pow (tan x) 3) (tan x))) (pow (tan x) 2))
1.0ms	x	@	inf	(+ (* eps (+ (pow (tan x) 3) (tan x))) (pow (tan x) 2))
1.0ms	eps	@	0	(+ (* eps (+ (pow (tan x) 3) (tan x))) (pow (tan x) 2))
1.0ms	eps	@	0	(* (* eps eps) (+ (* x (* x 4/3)) 1/3))

simplify326.0ms (2.1%)

Memory

-24.9MiB live, 451.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 728×	`lower-fma.f64`
10 728×	`lower-fma.f32`
6 224×	`lower-*.f64`
6 224×	`lower-*.f32`
3 298×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	17011
1	1205	16641
2	4144	14670
0	8372	14031

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 562

Calls

Call 1

Inputs
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* 4/3 (* eps x))))))
(* x (+ eps (* x (+ 1 (* x (+ (* 2/3 x) (* 4/3 eps)))))))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (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)))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* 4/3 (* eps x))))))
(* x (+ eps (* x (+ 1 (* x (+ (* 2/3 x) (* 4/3 eps)))))))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
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))
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 3) (pow (cos x) 3))
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))
(* 4/3 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(* 4/3 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* 4/3 (pow x 2)))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))

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

rewrite377.0ms (2.4%)

Memory

5.3MiB live, 294.4MiB allocated

Rules

4 926×	`lower-fma.f32`
4 908×	`lower-fma.f64`
4 272×	`lower-*.f32`
4 262×	`lower-*.f64`
2 420×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1494
0	113	1460
1	621	1124
2	5708	1100
0	8171	1028

Stop Event

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

Counts

26 → 330

Calls

Call 1

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

Outputs
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(+.f64 (*.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(+.f64 (*.f64 eps (tan.f64 x)) (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 eps (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (tan.f64 x))) (.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (.f64 eps (tan.f64 x)))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 2 binary64)) (-.f64 (.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 (*.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(fma.f64 eps (tan.f64 x) (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 eps (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (tan.f64 x) eps (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(fma.f64 (tan.f64 x) (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 eps (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) eps (fma.f64 eps (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
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(+.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (*.f64 x x))
(+.f64 (fma.f64 x x (.f64 (.f64 eps eps) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (.f64 eps x))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))
(fma.f64 eps (.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) (fma.f64 eps x (*.f64 x x)))
(fma.f64 x x (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))
(fma.f64 (.f64 eps eps) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (fma.f64 eps x (*.f64 x x)))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 eps x (*.f64 x x)))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) eps (.f64 x x))
(fma.f64 (.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (fma.f64 eps x (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (*.f64 x x)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))))) (fma.f64 x (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 eps (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (*.f64 x x))))))
(/.f64 (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x))) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (*.f64 x x)))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x)))) (neg.f64 (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (*.f64 x x))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))))))
(.f64 (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)) (.f64 x x))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 4/3 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 4/3 binary64))) #s(literal 1/3 binary64))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64)) (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64))))
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x #s(literal 4/3 binary64)) x #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) #s(literal 4/9 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal -1/9 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64)) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) #s(literal 4/9 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64)) (.f64 (*.f64 x x) #s(literal 4/9 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal -1/9 binary64)) (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) #s(literal 4/9 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal -1/9 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 4/3 binary64)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) #s(literal 4/9 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal -1/9 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64/27 binary64) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal 1/9 binary64)) (.f64 (*.f64 x x) #s(literal 4/9 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16/9 binary64) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal -1/3 binary64))))

eval289.0ms (1.9%)

Memory: 12.7MiB live, 201.7MiB allocated
Compiler: Compiled 31 731 to 1 673 computations (94.7% saved)

prune250.0ms (1.6%)

Memory

-23.2MiB live, 182.4MiB allocated

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	1 082	12	1 094
Fresh	8	0	8
Picked	2	3	5
Done	0	2	2
Total	1 092	17	1 109

Accuracy

100.0%

Counts

1 109 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.8%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	99.3%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (pow.f64 #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)) #s(literal 2 binary64)) eps eps))
	99.8%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 (*.f64 eps (tan.f64 x)) (tan.f64 x) eps))
	99.2%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	99.2%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	99.1%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps eps))
	98.9%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (*.f64 x x)) eps eps))
✓	100.0%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.7%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 #s(approx (pow (tan x) 3) (.f64 x (.f64 x x))) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.2%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (pow (tan x) 3) (tan x))) (pow (tan x) 2)) (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) (.f64 eps #s(literal 4/3 binary64))) #s(literal 1 binary64)) eps)))) eps))
	99.0%	#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps (+ (pow (tan x) 3) (tan x))) (pow (tan x) 2)) (*.f64 x (+.f64 x eps)))) eps))
✓	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
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Compiler

Compiled 1 267 to 337 computations (73.4% saved)

regimes57.0ms (0.4%)

Memory

-1.2MiB live, 39.6MiB allocated

Counts

44 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

31.0ms	x
12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.3%)

Memory

-3.1MiB live, 35.9MiB allocated

Counts

43 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory

32.3MiB live, 32.3MiB allocated

Counts

39 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

7.2MiB live, 45.9MiB allocated

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

-63.4MiB live, 45.2MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

17.0ms	x
7.0ms	eps
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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

18.8MiB live, 18.8MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps
6.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

-13.9MiB live, 24.1MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`eps`
99.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
99.1%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Memory

-21.1MiB live, 17.7MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Outputs
#s(approx (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) 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
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

7.6MiB live, 7.6MiB 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 (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -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 (+ (/ (sin x) (cos x)) (pow (/ (sin x) (cos x)) 3))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 x eps))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify34.0ms (0.2%)

Memory

-24.8MiB live, 14.8MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
14×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	869
1	170	869
2	174	869
3	176	869
4	177	869

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (8.4%)

Memory

41.4MiB live, 1 068.4MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
10 728×	`lower-fma.f64`
10 728×	`lower-fma.f32`
8 468×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1494
0	113	1460
1	621	1124
2	5708	1100
0	8171	1028
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	79	1106
0	128	1054
1	584	723
2	5543	723
0	8679	678
0	157	1351
1	464	1285
2	1534	1274
3	5949	1242
0	8534	1195
0	574	14740
1	1863	14357
2	6213	14030
0	8954	13412
0	452	9017
1	1386	8701
2	4477	8604
0	8118	8261
0	366	17011
1	1205	16641
2	4144	14670
0	8372	14031

Stop Event

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

Compiler

Compiled 582 to 271 computations (53.4% saved)

preprocess133.0ms (0.9%)

Memory: -29.8MiB live, 171.4MiB allocated
Compiler: Compiled 586 to 214 computations (63.5% 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%)

analyze55.0ms (0.4%)

sample7.4s (47.9%)

explain92.0ms (0.6%)

preprocess50.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize48.0ms (0.3%)

series35.0ms (0.2%)

simplify283.0ms (1.8%)

rewrite265.0ms (1.7%)

eval62.0ms (0.4%)

prune54.0ms (0.3%)

simplify243.0ms (1.6%)

localize322.0ms (2.1%)

series72.0ms (0.5%)

simplify247.0ms (1.6%)

rewrite493.0ms (3.2%)

eval176.0ms (1.1%)

prune118.0ms (0.8%)

simplify280.0ms (1.8%)

localize329.0ms (2.1%)

series92.0ms (0.6%)

simplify282.0ms (1.8%)

rewrite295.0ms (1.9%)

eval209.0ms (1.3%)

prune134.0ms (0.9%)

simplify392.0ms (2.5%)

localize316.0ms (2%)

series83.0ms (0.5%)

simplify326.0ms (2.1%)

rewrite377.0ms (2.4%)

eval289.0ms (1.9%)

prune250.0ms (1.6%)

regimes57.0ms (0.4%)

regimes51.0ms (0.3%)

regimes34.0ms (0.2%)

regimes35.0ms (0.2%)

regimes35.0ms (0.2%)

regimes21.0ms (0.1%)

regimes21.0ms (0.1%)

regimes13.0ms (0.1%)

regimes25.0ms (0.2%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify34.0ms (0.2%)

soundness1.3s (8.4%)

preprocess133.0ms (0.9%)

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