Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze75.0ms (0.5%)

Memory

-30.0MiB live, 92.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.3s (45.2%)

Memory

-122.1MiB live, 7 316.1MiB allocated

Samples

3.4s	26 362×	0	invalid
662.0ms	5 574×	0	valid
478.0ms	2 682×	1	valid

Precisions

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

const: 696.0ms (21.1% of total)

ival-tan: 629.0ms (19.1% of total)

ival-add: 513.0ms (15.5% of total)

ival-mult: 287.0ms (8.7% of total)

ival-<=: 256.0ms (7.8% of total)

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

ival-fabs: 223.0ms (6.8% of total)

ival-sub: 203.0ms (6.1% of total)

ival-and: 106.0ms (3.2% of total)

adjust: 88.0ms (2.7% of total)

exact: 47.0ms (1.4% of total)

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

Bogosity

explain127.0ms (0.9%)

Memory

-6.3MiB live, 77.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	2	(-1.889798177677739e-146 1.227075656794296e-150)	5	(-1.2048120858646896e-35 1.3912270648591378e-37)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
2	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	221	9
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	220	6
-	2	28

Precision

0.990990990990991

Recall

0.9734513274336283

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	6	0
-	2	3	25

Precision?

0.9783549783549783

Recall?

1.0

Freqs

test

number	freq
0	34
1	221
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	168×	1	valid
17.0ms	340×	0	valid
2.0ms	4×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

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

ival-tan: 10.0ms (48.2% of total)

adjust: 4.0ms (19.3% of total)

ival-add: 3.0ms (14.5% of total)

ival-sub: 3.0ms (14.5% of total)

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

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

preprocess53.0ms (0.4%)

Memory

-20.6MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (0.2%)

Memory

20.9MiB live, 20.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.11134085724335945	(tan.f64 (+.f64 x eps))
accuracy	24.105744961906762	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

9.0ms	84×	1	valid
9.0ms	170×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-tan: 5.0ms (44.5% of total)

adjust: 2.0ms (17.8% of total)

ival-add: 2.0ms (17.8% of total)

ival-sub: 2.0ms (17.8% of total)

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

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

series32.0ms (0.2%)

Memory

-26.7MiB live, 11.3MiB 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 (* 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 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 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 (- (/ (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 (+ 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 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 (- (/ (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 (- 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 -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 (/ (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) (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 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 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 (+ 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 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 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 (/ (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 (- 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 (/ (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 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 (/ (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

6 calls:

Time	Variable		Point	Expression
21.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify185.0ms (1.3%)

Memory

27.7MiB live, 110.5MiB 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	5964	1242
0	8538	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

Inputs
(* 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 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)))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (/ (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 (- 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
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* 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) (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)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
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 (+ 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 x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos 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)))
(/ (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))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

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

rewrite264.0ms (1.9%)

Memory

-24.3MiB live, 169.9MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 259

Calls

Call 1

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

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

eval41.0ms (0.3%)

Memory: 2.8MiB live, 81.8MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune73.0ms (0.5%)

Memory

64.5MiB live, 156.0MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	317	19	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	317	20	337

Accuracy

100.0%

Counts

337 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.3%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
	62.1%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	62.1%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
	62.3%	(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	62.1%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	61.2%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	33.6%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	62.1%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	62.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	62.1%	(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x))) (tan.f64 x))
	22.9%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
▶	61.4%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	61.0%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
▶	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 911 to 458 computations (49.7% saved)

simplify173.0ms (1.2%)

Memory

-42.8MiB live, 186.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))
cost-diff	320	(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff	704	(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff	16128	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	384	(-.f64 (+.f64 eps 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff	0	#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))

Rules

8 866×	`lower-fma.f32`
8 854×	`lower-fma.f64`
4 698×	`lower-*.f32`
4 686×	`lower-*.f64`
2 372×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	753
0	109	711
1	195	637
2	412	623
3	1187	620
4	5402	620
0	8213	610

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (1.7%)

Memory

-3.5MiB live, 389.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19207001953688405	(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))
accuracy	24.667504926362817	(-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)))
accuracy	30.21305601241581	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
accuracy	0.00390625	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.06652107453094697	(cos.f64 (+.f64 eps x))
accuracy	24.216121443082162	(-.f64 (+.f64 eps x) x)
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	0.11134085724335945	(tan.f64 (+.f64 x eps))
accuracy	0.1953125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy	24.105744961906762	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
accuracy	0.00390625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
accuracy	0.11134085724335945	(tan.f64 (+.f64 x eps))
accuracy	1.1022559112293453	#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
accuracy	24.105744961906762	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
accuracy	0.021816259768442016	(pow.f64 (sin.f64 x) #s(literal 4 binary64))
accuracy	0.1015625	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.22036880281590726	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.96875	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

88.0ms	87×	1	valid
88.0ms	167×	0	valid
3.0ms	2×	3	valid

Compiler

Compiled 681 to 61 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 142.0ms

ival-add: 29.0ms (20.4% of total)

ival-mult: 21.0ms (14.8% of total)

ival-div: 19.0ms (13.4% of total)

adjust: 15.0ms (10.6% of total)

const: 13.0ms (9.1% of total)

ival-tan: 12.0ms (8.4% of total)

ival-pow: 9.0ms (6.3% of total)

ival-sub: 8.0ms (5.6% of total)

ival-pow2: 6.0ms (4.2% of total)

ival-cos: 4.0ms (2.8% of total)

ival-sin: 4.0ms (2.8% of total)

exact: 1.0ms (0.7% of total)

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

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

series118.0ms (0.8%)

Memory

22.3MiB live, 138.4MiB allocated

Counts

26 → 528

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (/ 1 (/ 1 (tan x))) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (* (+ (* (* x x) 1/3) 1) x) (/ 1 (tan x)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))))
16.0ms	eps	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (/ 1 (/ 1 (tan x))) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (* (+ (* (* x x) 1/3) 1) x) (/ 1 (tan x)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))))
13.0ms	eps	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (/ 1 (/ 1 (tan x))) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (* (+ (* (* x x) 1/3) 1) x) (/ 1 (tan x)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))))
11.0ms	x	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (/ 1 (/ 1 (tan x))) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (* (+ (* (* x x) 1/3) 1) x) (/ 1 (tan x)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))))
9.0ms	x	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (/ 1 (/ 1 (tan x))) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (* (+ (* (* x x) 1/3) 1) x) (/ 1 (tan x)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))))

simplify247.0ms (1.8%)

Memory

-24.1MiB live, 276.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 322×	`lower-fma.f64`
10 322×	`lower-fma.f32`
7 580×	`lower-*.f64`
7 580×	`lower-*.f32`
5 338×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	776	13873
1	2526	13232
0	8456	12890

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 488

Calls

Call 1

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

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

rewrite220.0ms (1.6%)

Memory

-7.2MiB live, 185.7MiB allocated

Rules

4 746×	`lower-*.f32`
4 734×	`lower-*.f64`
4 336×	`lower-fma.f32`
4 324×	`lower-fma.f64`
2 342×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	480
0	109	435
1	508	335
2	4476	327
0	8161	315

Stop Event

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

Counts

26 → 786

Calls

Call 1

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

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

eval268.0ms (1.9%)

Memory: 9.4MiB live, 318.4MiB allocated
Compiler: Compiled 57 954 to 3 449 computations (94% saved)

prune302.0ms (2.2%)

Memory

3.0MiB live, 283.8MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 594	15	1 609
Fresh	11	3	14
Picked	5	0	5
Done	0	1	1
Total	1 610	19	1 629

Accuracy

100.0%

Counts

1 629 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	61.2%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	99.6%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	62.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	60.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))))
▶	60.1%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 #s(literal 1 binary64) x))))
✓	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	99.9%	(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
▶	99.9%	(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
	99.0%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.5%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (+.f64 (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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps)))

Compiler

Compiled 745 to 418 computations (43.9% saved)

simplify137.0ms (1%)

Memory

2.3MiB live, 112.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

12 370×	`lower-fma.f32`
12 366×	`lower-fma.f64`
4 570×	`lower-*.f32`
4 558×	`lower-*.f64`
2 578×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	448
0	103	424
1	178	382
2	423	375
3	1591	375
4	4213	375
0	8412	359

Stop Event

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

Calls

Call 1

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

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

localize304.0ms (2.2%)

Memory

-2.7MiB live, 240.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))))
accuracy	0.00390625	(+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))
accuracy	0.11407394579730011	(cos.f64 (+.f64 (+.f64 eps x) x))
accuracy	0.28125	(+.f64 (+.f64 eps x) x)
accuracy	0.00390625	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.06652107453094697	(cos.f64 (+.f64 eps x))
accuracy	0.2200684961533617	#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
accuracy	0.11134085724335945	(tan.f64 (+.f64 x eps))
accuracy	0.1953125	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 #s(literal 1 binary64) x)))
accuracy	1.3150010014677702	#s(approx (/ 1 (tan x)) (/.f64 #s(literal 1 binary64) x))
accuracy	24.105744961906762	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 #s(literal 1 binary64) x))))
accuracy	0.00390625	(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps)
accuracy	0.0859375	(.f64 (.f64 eps eps) eps)
accuracy	0.22036880281590726	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps)))
accuracy	1.1759725309094728	#s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps))
accuracy	0.0078125	(/.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.01171875	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
accuracy	0.01171875	(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	0.06652107453094697	(cos.f64 (+.f64 eps x))

Samples

162.0ms	88×	1	valid
80.0ms	166×	0	valid
3.0ms	2×	3	valid

Compiler

Compiled 323 to 70 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 180.0ms

ival-pow2: 45.0ms (25.1% of total)

ival-mult: 29.0ms (16.2% of total)

ival-div: 23.0ms (12.8% of total)

ival-add: 18.0ms (10% of total)

adjust: 14.0ms (7.8% of total)

const: 10.0ms (5.6% of total)

ival-sin: 10.0ms (5.6% of total)

ival-cos: 9.0ms (5% of total)

ival-pow: 9.0ms (5% of total)

ival-sub: 7.0ms (3.9% of total)

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

exact: 1.0ms (0.6% of total)

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

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

series61.0ms (0.4%)

Memory

15.4MiB live, 86.2MiB allocated

Counts

25 → 492

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	inf	((* (/ (sin (+ 0 eps)) (cos (+ eps x))) (/ 1 (cos x))) (+ 0 eps) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* eps eps) eps) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (tan (+ x eps)) (+ x eps) (/ 1 (/ 1 (tan x))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (cos (+ eps x)) (/ 1 (cos x)) (/ 1 (tan x)) (* (cos (+ eps x)) (cos x)) (+ (+ eps x) x) (cos (+ (+ eps x) x)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x))))
6.0ms	x	@	-inf	((* (/ (sin (+ 0 eps)) (cos (+ eps x))) (/ 1 (cos x))) (+ 0 eps) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* eps eps) eps) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (tan (+ x eps)) (+ x eps) (/ 1 (/ 1 (tan x))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (cos (+ eps x)) (/ 1 (cos x)) (/ 1 (tan x)) (* (cos (+ eps x)) (cos x)) (+ (+ eps x) x) (cos (+ (+ eps x) x)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x))))
5.0ms	eps	@	-inf	((* (/ (sin (+ 0 eps)) (cos (+ eps x))) (/ 1 (cos x))) (+ 0 eps) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* eps eps) eps) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (tan (+ x eps)) (+ x eps) (/ 1 (/ 1 (tan x))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (cos (+ eps x)) (/ 1 (cos x)) (/ 1 (tan x)) (* (cos (+ eps x)) (cos x)) (+ (+ eps x) x) (cos (+ (+ eps x) x)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x))))
5.0ms	eps	@	0	((* (/ (sin (+ 0 eps)) (cos (+ eps x))) (/ 1 (cos x))) (+ 0 eps) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* eps eps) eps) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (tan (+ x eps)) (+ x eps) (/ 1 (/ 1 (tan x))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (cos (+ eps x)) (/ 1 (cos x)) (/ 1 (tan x)) (* (cos (+ eps x)) (cos x)) (+ (+ eps x) x) (cos (+ (+ eps x) x)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x))))
5.0ms	x	@	0	((* (/ (sin (+ 0 eps)) (cos (+ eps x))) (/ 1 (cos x))) (+ 0 eps) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* eps eps) eps) (- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) (tan (+ x eps)) (+ x eps) (/ 1 (/ 1 (tan x))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (cos (+ eps x)) (/ 1 (cos x)) (/ 1 (tan x)) (* (cos (+ eps x)) (cos x)) (+ (+ eps x) x) (cos (+ (+ eps x) x)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x))))

simplify205.0ms (1.5%)

Memory

8.7MiB live, 245.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 408×	`lower-fma.f64`
9 408×	`lower-fma.f32`
6 366×	`lower-*.f64`
6 366×	`lower-*.f32`
3 804×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	666	7809
1	2083	7542
2	6750	7437
0	8079	7111

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 466

Calls

Call 1

Inputs
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
eps
eps
eps
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eps
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eps
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x
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eps
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eps
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1
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(* 2 x)
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eps
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(* 2 (/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))))
(* 2 (/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))))
(* 2 (/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))))
(/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps)))))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(cos (- (* 2 x) (* -1 eps)))
(+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))
(+ (cos (neg (* -1 eps))) (cos (- (* 2 x) (* -1 eps))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ 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)))))
(/ (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) (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)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
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 eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (+ (* -2 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* -2 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)))))) (* -2 (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(* 1/2 (/ (sin eps) (cos eps)))
(+ (* 1/2 (/ (sin eps) (cos eps))) (* 1/2 (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))))
(+ (* 1/2 (/ (sin eps) (cos eps))) (* x (- (* -1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))
(+ (* 1/2 (/ (sin eps) (cos eps))) (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)))))) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 5/24 (* 61/720 (pow x 2)))))))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(cos eps)
(+ (cos eps) (* -2 (* x (sin eps))))
(+ (cos eps) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
(+ (cos eps) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
(* 2 (cos eps))
(+ (* -2 (* x (sin eps))) (* 2 (cos eps)))
(+ (* 2 (cos eps)) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
(+ (* 2 (cos eps)) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps 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 x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -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)))
(/ (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))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))

Outputs
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(pow eps 3)
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(pow eps 3)
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(* eps (- 1 (* -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))))) (/ (sin x) (cos x)))
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x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* 2 (/ eps (+ 1 (cos (* 2 x)))))
(/.f64 (.f64 #s(literal 2 binary64) eps) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))
(* eps (+ (* 2 (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(.f64 (fma.f64 (.f64 #s(literal 2 binary64) eps) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)
(* eps (+ (* eps (+ (* 2 (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x)))))))))) (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(.f64 (fma.f64 (.f64 #s(literal 2 binary64) eps) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))))) eps (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)
(* eps (+ (* eps (+ (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* eps (+ (* -2 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 2 (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 eps (.f64 #s(literal -2 binary64) eps)) (-.f64 (fma.f64 (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) #s(literal 1/6 binary64) (/.f64 (.f64 (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 2 binary64) x))) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))))) (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))))) (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))))) eps (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) #s(literal 2 binary64))) eps (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)
(/ eps (+ 1 (cos (* 2 x))))
(/.f64 eps (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))
(* eps (+ (/ 1 (+ 1 (cos (* 2 x)))) (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))))
(.f64 (fma.f64 (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) eps (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 x))))))
(fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))))) eps (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) (.f64 eps eps) (/.f64 eps (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2)))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 x))))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (-.f64 (fma.f64 (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) #s(literal 1/6 binary64) (/.f64 (.f64 (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 2 binary64) x))) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))))) (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (tan.f64 (/.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) (fma.f64 (/.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (pow.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))))))) eps (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) (.f64 eps eps) (/.f64 eps (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) (sin.f64 x)) eps (cos.f64 x))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(cos (* 2 x))
(cos.f64 (*.f64 #s(literal -2 binary64) x))
(+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x)))))
(fma.f64 (neg.f64 eps) (sin.f64 (.f64 #s(literal 2 binary64) x)) (cos.f64 (.f64 #s(literal -2 binary64) x)))
(+ (cos (* 2 x)) (* eps (- (* -1/2 (* eps (cos (* 2 x)))) (sin (* 2 x)))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 (.f64 #s(literal -2 binary64) x))) (sin.f64 (.f64 #s(literal 2 binary64) x))) eps (cos.f64 (*.f64 #s(literal -2 binary64) x)))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x)))))) (sin (* 2 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 (.f64 #s(literal 2 binary64) x)))) eps (cos.f64 (.f64 #s(literal -2 binary64) x)))
(+ 1 (cos (* 2 x)))
(+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))
(+ 1 (+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x))))))
(fma.f64 (neg.f64 eps) (sin.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))
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(* eps (+ 1 (/ x eps)))
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(* eps (+ 1 (/ x eps)))
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(/.f64 (sin.f64 eps) (cos.f64 eps))
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eps
(+ eps x)
(+.f64 x eps)
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(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
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(/ (sin eps) (cos eps))
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1
#s(literal 1 binary64)
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(/ 1 x)
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(/ (+ 1 (* -1/3 (pow x 2))) x)
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(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
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eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -2 (* x (sin eps))))
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(+ (cos eps) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
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(* 2 (cos eps))
(*.f64 (cos.f64 eps) #s(literal 2 binary64))
(+ (* -2 (* x (sin eps))) (* 2 (cos eps)))
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(/ (sin eps) (* (cos x) (cos (+ eps x))))
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(sin eps)
(sin.f64 eps)
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (-.f64 #s(literal -2 binary64) (/.f64 eps x)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (-.f64 #s(literal -2 binary64) (/.f64 eps x)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (-.f64 #s(literal -2 binary64) (/.f64 eps x)) (neg.f64 x))
(cos (- eps (* -2 x)))
(cos.f64 (fma.f64 #s(literal 2 binary64) x eps))
(cos (- eps (* -2 x)))
(cos.f64 (fma.f64 #s(literal 2 binary64) x eps))
(cos (- eps (* -2 x)))
(cos.f64 (fma.f64 #s(literal 2 binary64) x eps))
(cos (- eps (* -2 x)))
(cos.f64 (fma.f64 #s(literal 2 binary64) x eps))
(+ (cos eps) (cos (- eps (* -2 x))))
(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
(+ (cos eps) (cos (- eps (* -2 x))))
(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
(+ (cos eps) (cos (- eps (* -2 x))))
(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
(+ (cos eps) (cos (- eps (* -2 x))))
(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))

rewrite183.0ms (1.3%)

Memory

9.7MiB live, 242.2MiB allocated

Rules

4 946×	`lower-*.f32`
4 946×	`lower-fma.f32`
4 942×	`lower-fma.f64`
4 934×	`lower-*.f64`
2 536×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	394
0	103	362
1	529	300
2	5103	300
0	8235	282

Stop Event

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

Counts

25 → 663

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sin.f64 eps)) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))))) (-.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (sin.f64 eps)) (+.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (-.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))))
(.f64 (/.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) #s(literal 1/2 binary64))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))))
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (sin.f64 eps) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(pow.f64 (/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)) (*.f64 #s(literal 2 binary64) (sin.f64 eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (/.f64 (sin.f64 eps) (cos.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (cos.f64 x) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) #s(literal 2 binary64)) (neg.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (sin.f64 eps))) (neg.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 eps))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)) (neg.f64 (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x)))) (-.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))))
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x))) (.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (sin.f64 eps))) (neg.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 x))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps))) (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps))) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))))
(/.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64)) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (.f64 (sin.f64 eps) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (cos.f64 x)))
(/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 eps)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (neg.f64 (cos.f64 x))))
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)) (sin.f64 eps)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)) (*.f64 #s(literal 2 binary64) (sin.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (/.f64 (sin.f64 eps) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(fma.f64 #s(literal -1 binary64) (tan.f64 x) (tan.f64 (+.f64 x eps)))
(fma.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (tan.f64 x)))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x)))
(-.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 (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)))))
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(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
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eval222.0ms (1.6%)

Memory: -0.9MiB live, 238.4MiB allocated
Compiler: Compiled 31 457 to 2 953 computations (90.6% saved)

prune195.0ms (1.4%)

Memory

5.3MiB live, 286.8MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	1 296	14	1 310
Fresh	7	6	13
Picked	3	2	5
Done	0	1	1
Total	1 306	23	1 329

Accuracy

100.0%

Counts

1 329 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.5%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
▶	99.4%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)))
	62.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	60.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))))
✓	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	99.9%	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
	49.9%	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
▶	100.0%	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (*.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps))))) #s(literal 2 binary64))
▶	99.9%	(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))) #s(literal 2 binary64))
	99.6%	(.f64 (/.f64 #s(approx (sin (+ 0 eps)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
	99.0%	(.f64 #s(approx (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (/.f64 eps (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (.f64 (fma.f64 (/.f64 (tan.f64 (/.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) eps (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	99.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
▶	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps)))
	45.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) eps) (.f64 eps eps)))))
▶	6.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))))

Compiler

Compiled 844 to 494 computations (41.5% saved)

simplify165.0ms (1.2%)

Memory

-38.0MiB live, 180.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))) #s(literal 2 binary64))
cost-diff	0	#s(approx (+ (* (* eps eps) -1/6) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps))
cost-diff	0	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	0	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x)))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
cost-diff	64	(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps)
cost-diff	0	(.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64))))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))))
cost-diff	0	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (*.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps))))) #s(literal 2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	6400	(+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps))))

Rules

12 920×	`lower-fma.f32`
12 910×	`lower-fma.f64`
4 750×	`lower-*.f32`
4 726×	`lower-*.f64`
3 074×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	870
0	136	854
1	242	767
2	585	757
3	2100	757
4	5093	757
0	8729	727

Stop Event

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

Calls

Call 1

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

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

localize331.0ms (2.4%)

Memory

36.8MiB live, 306.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 eps)
accuracy	0.00390625	(/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps)))
accuracy	0.00390625	(+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))
accuracy	0.11407394579730011	(cos.f64 (fma.f64 #s(literal 2 binary64) x eps))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.06652107453094697	(cos.f64 (+.f64 eps x))
accuracy	0.2200684961533617	#s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps))
accuracy	0.3460843215374133	#s(approx (+ (* (* eps eps) -1/6) 1) #s(literal 1 binary64))
accuracy	0.1484375	(*.f64 eps (+.f64 x eps))
accuracy	0.22036880281590726	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
accuracy	0.34375	(*.f64 #s(literal 1/3 binary64) eps)
accuracy	1.2737642607660893	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x)))
accuracy	0.1015625	(.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64))
accuracy	0.22036880281590726	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))))
accuracy	1.1759725309094728	#s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64))))
accuracy	59.955502006227015	#s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))
accuracy	0.00390625	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps)))))
accuracy	0.00390625	(+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps))))
accuracy	0.00390625	(cos.f64 (+.f64 x x))
accuracy	0.0078125	(-.f64 (.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps)))

Samples

150.0ms	84×	1	valid
125.0ms	171×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 594 to 85 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 244.0ms

adjust: 74.0ms (30.3% of total)

ival-mult: 65.0ms (26.6% of total)

ival-add: 25.0ms (10.2% of total)

ival-div: 15.0ms (6.1% of total)

ival-cos: 13.0ms (5.3% of total)

const: 12.0ms (4.9% of total)

ival-pow: 9.0ms (3.7% of total)

ival-sin: 9.0ms (3.7% of total)

ival-sub: 7.0ms (2.9% of total)

ival-tan: 7.0ms (2.9% of total)

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

exact: 1.0ms (0.4% of total)

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

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

series86.0ms (0.6%)

Memory

1.1MiB live, 76.6MiB allocated

Counts

28 → 564

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	eps	@	inf	((+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps)))) (+ 0 eps) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* (* eps eps) eps) 1/3) (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) 2) (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))) (cos (+ x x)) (* 1/3 eps) (* eps (+ x eps)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (cos (+ (* 2 x) eps)) (cos eps))
8.0ms	eps	@	-inf	((+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps)))) (+ 0 eps) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* (* eps eps) eps) 1/3) (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) 2) (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))) (cos (+ x x)) (* 1/3 eps) (* eps (+ x eps)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (cos (+ (* 2 x) eps)) (cos eps))
8.0ms	x	@	-inf	((+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps)))) (+ 0 eps) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* (* eps eps) eps) 1/3) (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) 2) (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))) (cos (+ x x)) (* 1/3 eps) (* eps (+ x eps)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (cos (+ (* 2 x) eps)) (cos eps))
7.0ms	x	@	inf	((+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps)))) (+ 0 eps) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* (* eps eps) eps) 1/3) (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) 2) (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))) (cos (+ x x)) (* 1/3 eps) (* eps (+ x eps)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (cos (+ (* 2 x) eps)) (cos eps))
4.0ms	eps	@	0	((+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps)))) (+ 0 eps) (* (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) 2) (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (* (* eps eps) eps) 1/3) eps) (* (* (* eps eps) eps) 1/3) (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) 2) (/ (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps))) (sin eps) (+ (cos (+ (* 2 x) eps)) (cos eps)) (- (* (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))) (cos (+ x x)) (* 1/3 eps) (* eps (+ x eps)) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (cos (+ (* 2 x) eps)) (cos eps))

simplify243.0ms (1.7%)

Memory

7.6MiB live, 292.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 356×	`lower-fma.f64`
10 356×	`lower-fma.f32`
6 658×	`lower-*.f64`
6 658×	`lower-*.f32`
3 900×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	660	11561
1	2096	11209
2	6833	11056
0	8099	10510

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 546

Calls

Call 1

Inputs
(+ 1 (cos (* 2 x)))
(+ 1 (+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (* -1/2 (cos (* 2 x))) 1/2)) (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x))))) 1/2)) (sin (* 2 x))))))
eps
eps
eps
eps
(* 2 (/ eps (+ 1 (cos (* 2 x)))))
(* eps (+ (* 2 (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(* eps (+ (* eps (+ (* 2 (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x)))))))))) (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(* eps (+ (* eps (+ (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* eps (+ (* -2 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 2 (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(/ eps (+ 1 (cos (* 2 x))))
(* eps (+ (/ 1 (+ 1 (cos (* 2 x)))) (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 x))))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2)))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 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)))))
(* 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)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(* 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)))))
(* 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 (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)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* 2 (/ eps (+ 1 (cos (* 2 x)))))
(* eps (+ (* 2 (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(* eps (+ (* eps (+ (* 2 (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x)))))))))) (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(* eps (+ (* eps (+ (* 2 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* eps (+ (* -2 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 2 (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))))))) (* 2 (/ 1 (+ 1 (cos (* 2 x)))))))
(/ eps (+ 1 (cos (* 2 x))))
(* eps (+ (/ 1 (+ 1 (cos (* 2 x)))) (/ (* eps (sin (* 2 x))) (pow (+ 1 (cos (* 2 x))) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 x))))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin (* 2 x)) (- (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (+ 1 (cos (* 2 x))))) (+ (* 1/6 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (/ (* (sin (* 2 x)) (- (* -1/2 (cos (* 2 x))) 1/2)) (pow (+ 1 (cos (* 2 x))) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (cos (* 2 x))) 2)))) (+ (* -1 (/ (pow (sin (* 2 x)) 2) (pow (+ 1 (cos (* 2 x))) 3))) (+ (* -1/2 (/ (cos (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))) (* 1/6 (/ 1 (+ 1 (cos (* 2 x))))))))) (* -1 (/ (sin (* 2 x)) (pow (+ 1 (cos (* 2 x))) 2))))) (/ 1 (+ 1 (cos (* 2 x))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (cos (* 2 x)))
(+ 1 (+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (* -1/2 (cos (* 2 x))) 1/2)) (sin (* 2 x))))))
(+ 1 (+ (cos (* 2 x)) (* eps (- (* eps (- (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x))))) 1/2)) (sin (* 2 x))))))
(cos (* 2 x))
(+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* -1/2 (* eps (cos (* 2 x)))) (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x)))))) (sin (* 2 x)))))
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(cos (* 2 x))
(+ (cos (* 2 x)) (* -1 (* eps (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* -1/2 (* eps (cos (* 2 x)))) (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -1/2 (cos (* 2 x))) (* 1/6 (* eps (sin (* 2 x)))))) (sin (* 2 x)))))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
eps
eps
eps
eps
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (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))))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
(* 1/3 (pow eps 3))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(- (/ (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)))
(* (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 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))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
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(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
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(* 1/3 eps)
(* 1/3 eps)
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(- (+ (cos (neg (* -1 eps))) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
eps
eps
eps
eps
(* 2 (/ (sin (neg (* -1 eps))) (- (+ (cos (neg (* -1 eps))) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin (neg (* -1 eps))) (- (+ (cos (neg (* -1 eps))) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin (neg (* -1 eps))) (- (+ (cos (neg (* -1 eps))) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
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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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(* 1/3 (pow eps 3))
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(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(* -1/6 (pow eps 3))
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(* -1/6 (pow eps 2))
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(* 2 (cos eps))
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(/ (sin eps) (cos eps))
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(+ (* x (+ (* x (+ (* -2 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)))))) (* -2 (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
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(/ (sin eps) (cos eps))
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eps
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(/ (sin eps) (cos eps))
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(sin eps)
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(sin eps)
(sin eps)
(/ (sin eps) (cos eps))
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(* 1/2 (/ (sin eps) (cos eps)))
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(+ (* 1/2 (/ (sin eps) (cos eps))) (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)))))) (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/2 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))
(* 2 (cos eps))
(+ (* -2 (* x (sin eps))) (* 2 (cos eps)))
(+ (* 2 (cos eps)) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
(+ (* 2 (cos eps)) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
(cos eps)
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(+ (cos eps) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
1
(+ 1 (* -2 (pow x 2)))
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(pow eps 2)
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(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(cos eps)
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(cos eps)
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(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(cos eps)
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(+ (cos eps) (* x (- (* -2 (* x (cos eps))) (* 2 (sin eps)))))
(+ (cos eps) (* x (- (* x (+ (* -2 (cos eps)) (* 4/3 (* x (sin eps))))) (* 2 (sin eps)))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (* 2 x)))) (* (sin eps) (sin (* 2 x)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ 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)))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(- (/ (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)))
(+ 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 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x))))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(/ (sin eps) (+ (cos eps) (cos (+ eps (* 2 x)))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(+ (cos eps) (cos (+ eps (* 2 x))))
(- (* (cos eps) (cos (* 2 x))) (* (sin eps) (sin (* 2 x))))
(- (* (cos eps) (cos (* 2 x))) (* (sin eps) (sin (* 2 x))))
(- (* (cos eps) (cos (* 2 x))) (* (sin eps) (sin (* 2 x))))
(- (* (cos eps) (cos (* 2 x))) (* (sin eps) (sin (* 2 x))))
(cos (* 2 x))
(cos (* 2 x))
(cos (* 2 x))
(cos (* 2 x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(cos (+ eps (* 2 x)))
(- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))
(- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))
(- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))
(- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))))
(* 2 (/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x)))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 x))))))
(/ (sin eps) (- (+ (cos eps) (* (cos eps) (cos (neg (* -2 x))))) (* (sin eps) (sin (neg (* -2 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 (* 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)))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(- (/ (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 (* 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 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(* 2 (/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x))))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(/ (sin eps) (+ (cos eps) (cos (- eps (* -2 x)))))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))
(+ (cos eps) (cos (- eps (* -2 x))))
(- (* (cos eps) (cos (neg (* -2 x)))) (* (sin eps) (sin (neg (* -2 x)))))
(- (* (cos eps) (cos (neg (* -2 x)))) (* (sin eps) (sin (neg (* -2 x)))))
(- (* (cos eps) (cos (neg (* -2 x)))) (* (sin eps) (sin (neg (* -2 x)))))
(- (* (cos eps) (cos (neg (* -2 x)))) (* (sin eps) (sin (neg (* -2 x)))))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))
(cos (- eps (* -2 x)))

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

rewrite264.0ms (1.9%)

Memory

15.2MiB live, 361.7MiB allocated

Rules

4 768×	`lower-fma.f32`
4 758×	`lower-fma.f64`
4 534×	`lower-*.f32`
4 512×	`lower-*.f64`
2 894×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	761
0	136	695
1	662	565
2	6311	565
0	8570	526

Stop Event

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

Counts

28 → 564

Calls

Call 1

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

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

eval251.0ms (1.8%)

Memory: -20.0MiB live, 257.1MiB allocated
Compiler: Compiled 39 115 to 3 223 computations (91.8% saved)

prune216.0ms (1.6%)

Memory

20.0MiB live, 370.9MiB allocated

Pruning

29 alts after pruning (22 fresh and 7 done)

	Pruned	Kept	Total
New	1 218	13	1 231
Fresh	6	9	15
Picked	1	4	5
Done	0	3	3
Total	1 225	29	1 254

Accuracy

100.0%

Counts

1 254 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	99.4%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.4%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
	62.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	60.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x))))
✓	62.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	99.9%	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
	49.9%	(.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
	100.0%	(.f64 (/.f64 (sin.f64 eps) (fma.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 (+.f64 x x))))) #s(literal 2 binary64))
✓	99.9%	(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))) #s(literal 2 binary64))
	99.4%	(.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ (* (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)) (cos.f64 eps))) #s(literal 2 binary64))
	99.4%	(.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ (* (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
	99.6%	(.f64 (/.f64 #s(approx (sin (+ 0 eps)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ eps x) x)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) #s(literal 1 binary64)) eps)))
	99.0%	(.f64 #s(approx (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- ( (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (/.f64 eps (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (- ( (cos (+ x x)) (cos eps)) (* (sin (+ x x)) (sin eps))))) (.f64 (fma.f64 (/.f64 (tan.f64 (/.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))) eps (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) eps)) #s(literal 2 binary64))
	99.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
	50.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) (.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) eps #s(literal 1 binary64)) x eps) x))) eps)))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 #s(approx (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps x)) x))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 #s(approx (+ (* (+ (* 4/3 (* eps (+ x eps))) 1) x) eps) (.f64 (.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x))) eps eps))
	50.5%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) (+.f64 x eps)) eps #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps)))
	45.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) eps) (.f64 eps eps)))))
✓	6.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64)))))
	6.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 (*.f64 #s(literal 1/3 binary64) eps) eps) eps))))
	6.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) #s(approx (+ (* (* (* eps eps) eps) 1/3) eps) (.f64 (.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps)))))

Compiler

Compiled 1 749 to 607 computations (65.3% saved)

regimes67.0ms (0.5%)

Memory

3.1MiB live, 112.1MiB allocated

Counts

62 → 1

Calls

Call 1

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

Outputs

(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (-.f64 (*.f64 (cos.f64 (+.f64 x x)) (cos.f64 eps)) (*.f64 (sin.f64 (+.f64 x x)) (sin.f64 eps))))) #s(literal 2 binary64))

Calls

3 calls:

24.0ms	eps
22.0ms	x
18.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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)

regimes49.0ms (0.4%)

Memory

13.1MiB live, 90.0MiB allocated

Counts

56 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

regimes87.0ms (0.6%)

Memory

-16.1MiB live, 84.3MiB allocated

Counts

55 → 1

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))

Calls

3 calls:

40.0ms	x
30.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes44.0ms (0.3%)

Memory

8.9MiB live, 83.5MiB allocated

Counts

44 → 1

Calls

Call 1

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

Outputs
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))

Calls

3 calls:

15.0ms	eps
15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Memory

-4.7MiB live, 77.9MiB allocated

Counts

39 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	eps
11.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.4%)

Memory

-2.1MiB live, 36.6MiB allocated

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

31.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory

3.8MiB live, 43.0MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	eps
8.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes30.0ms (0.2%)

Memory

-29.1MiB live, 51.4MiB allocated

Counts

27 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	x
8.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes63.0ms (0.5%)

Memory

10.1MiB live, 46.2MiB allocated

Counts

26 → 1

Calls

Call 1

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

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

Calls

3 calls:

46.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory

-4.2MiB live, 34.0MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs
(.f64 #s(approx (/ (sin (+ 0 eps)) (+ (cos (+ 0 eps)) (cos (+ (+ eps x) x)))) (/.f64 eps (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)))) #s(literal 2 binary64))

Calls

3 calls:

11.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	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)

regimes14.0ms (0.1%)

Memory

29.2MiB live, 29.2MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`eps`
98.4%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.4%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-25.5MiB live, 19.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	x
3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
98.4%	1	`eps`
98.4%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.4%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 (*.f64 eps eps) eps) #s(literal 1/3 binary64) 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
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-20.7MiB live, 16.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Outputs

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

Calls

3 calls:

3.0ms	eps
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
6.2%	1	`x`
6.2%	1	`eps`
6.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative_binary64`
18×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	648
1	185	648
2	193	648
3	198	648
4	200	648

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (11.4%)

Memory

7.0MiB live, 880.7MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
10 356×	`lower-fma.f64`
10 356×	`lower-fma.f32`
10 322×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	666	7809
1	2083	7542
2	6750	7437
0	8079	7111
0	74	394
0	103	362
1	529	300
2	5103	300
0	8235	282
0	776	13873
1	2526	13232
0	8456	12890
0	93	761
0	136	695
1	662	565
2	6311	565
0	8570	526
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195
0	59	480
0	109	435
1	508	335
2	4476	327
0	8161	315
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	660	11561
1	2096	11209
2	6833	11056
0	8099	10510

Stop Event

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

Compiler

Compiled 787 to 392 computations (50.2% saved)

preprocess177.0ms (1.3%)

Memory: -6.8MiB live, 196.4MiB allocated
Compiler: Compiled 536 to 188 computations (64.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze75.0ms (0.5%)

sample6.3s (45.2%)

explain127.0ms (0.9%)

preprocess53.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize25.0ms (0.2%)

series32.0ms (0.2%)

simplify185.0ms (1.3%)

rewrite264.0ms (1.9%)

eval41.0ms (0.3%)

prune73.0ms (0.5%)

simplify173.0ms (1.2%)

localize235.0ms (1.7%)

series118.0ms (0.8%)

simplify247.0ms (1.8%)

rewrite220.0ms (1.6%)

eval268.0ms (1.9%)

prune302.0ms (2.2%)

simplify137.0ms (1%)

localize304.0ms (2.2%)

series61.0ms (0.4%)

simplify205.0ms (1.5%)

rewrite183.0ms (1.3%)

eval222.0ms (1.6%)

prune195.0ms (1.4%)

simplify165.0ms (1.2%)

localize331.0ms (2.4%)

series86.0ms (0.6%)

simplify243.0ms (1.7%)

rewrite264.0ms (1.9%)

eval251.0ms (1.8%)

prune216.0ms (1.6%)

regimes67.0ms (0.5%)

regimes49.0ms (0.4%)

regimes87.0ms (0.6%)

regimes44.0ms (0.3%)

regimes38.0ms (0.3%)

regimes51.0ms (0.4%)

regimes34.0ms (0.2%)

regimes30.0ms (0.2%)

regimes63.0ms (0.5%)

regimes26.0ms (0.2%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.6s (11.4%)

preprocess177.0ms (1.3%)

end0.0ms (0%)

Profiling

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

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