Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze68.0ms (0.4%)

Memory

2.5MiB live, 74.6MiB 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)

sample9.5s (62.7%)

Memory

-54.8MiB live, 10 231.5MiB allocated

Samples

3.9s	25 872×	0	invalid
3.2s	5 651×	2	valid
627.0ms	2 468×	1	valid
17.0ms	137×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.3s

ival-cos: 2.5s (39.8% of total)

const: 733.0ms (11.7% of total)

ival-<=: 680.0ms (10.8% of total)

adjust: 587.0ms (9.3% of total)

ival-sub: 371.0ms (5.9% of total)

ival-add: 371.0ms (5.9% of total)

ival-mult: 301.0ms (4.8% of total)

ival-<: 290.0ms (4.6% of total)

ival-fabs: 259.0ms (4.1% of total)

ival-and: 112.0ms (1.8% of total)

exact: 69.0ms (1.1% of total)

ival-assert: 14.0ms (0.2% of total)

Bogosity

explain313.0ms (2.1%)

Memory

-20.5MiB live, 138.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
140	116	(-3.361538306932203e-163 5.979618890699649e-176)	1	(1.481725682116547 0.0009059735583580095)	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	255	1

Confusion

	Predicted +	Predicted -
+	139	1
-	116	0

Precision

0.5450980392156862

Recall

0.9928571428571429

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	1	0
-	116	0	0

Precision?

0.546875

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

127.0ms	362×	2	valid
70.0ms	144×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 122.0ms

ival-cos: 94.0ms (77.1% of total)

adjust: 18.0ms (14.8% of total)

ival-sub: 6.0ms (4.9% of total)

ival-add: 3.0ms (2.5% of total)

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

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

preprocess25.0ms (0.2%)

Memory

14.1MiB live, 14.1MiB allocated

Algorithm

1×	egg-herbie

Rules

108×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
80×	`associate--r+`
66×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize93.0ms (0.6%)

Memory

7.1MiB live, 93.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.017910009768442016	(cos.f64 (+.f64 x eps))
accuracy	31.468000124163822	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

77.0ms	181×	2	valid
9.0ms	72×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-cos: 59.0ms (79.3% of total)

adjust: 10.0ms (13.4% of total)

ival-sub: 3.0ms (4% of total)

ival-add: 2.0ms (2.7% of total)

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

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

series6.0ms (0%)

Memory

-30.5MiB live, 8.9MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos eps) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify141.0ms (0.9%)

Memory

18.2MiB live, 135.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
4 148×	`lower-*.f64`
4 148×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin 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))))
x
(+ eps x)
(+ eps x)
(+ 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 x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x 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)))
(cos (- x (* -1 eps)))
(cos (- 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)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(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))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(cos x)
(cos x)
(cos 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))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- 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)))
(cos x)
(cos x)
(cos x)
(cos x)

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

rewrite157.0ms (1%)

Memory

5.6MiB live, 163.8MiB allocated

Rules

4 936×	`lower-fma.f64`
4 936×	`lower-fma.f32`
4 656×	`lower-*.f64`
4 656×	`lower-*.f32`
2 192×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (-.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))))
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(fma.f64 #s(literal -1 binary64) (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))) (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(cos.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(cos.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(cos.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))) (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(exp.f64 (*.f64 (log.f64 (cos.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (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) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (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 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))

eval35.0ms (0.2%)

Memory: -12.0MiB live, 65.1MiB allocated
Compiler: Compiled 6 943 to 892 computations (87.2% saved)

prune34.0ms (0.2%)

Memory

29.6MiB live, 68.8MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	298	8	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	298	9	307

Accuracy

99.8%

Counts

307 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	50.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	49.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 205 to 168 computations (18% saved)

simplify137.0ms (0.9%)

Memory

-9.6MiB live, 113.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
cost-diff	6400	(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(sin.f64 x)
cost-diff	0	(neg.f64 eps)
cost-diff	0	(*.f64 (neg.f64 eps) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

11 244×	`lower-fma.f32`
11 234×	`lower-fma.f64`
3 490×	`lower-*.f32`
3 468×	`lower-*.f64`
1 824×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	318
0	80	308
1	137	308
2	273	304
3	676	304
4	1500	304
5	2977	304
6	4171	304
7	5997	304
8	7164	304
9	7889	304
0	8026	295

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
eps
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
#s(literal 1/6 binary64)
(sin.f64 x)
x
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
eps
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 x) (neg.f64 eps))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(cos.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
#s(literal 1/6 binary64)
(sin.f64 x)
x
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

localize311.0ms (2.1%)

Memory

-13.9MiB live, 326.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.051174462261739065	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
accuracy	0.13671875	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.3515625	(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
accuracy	0.35546875	(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
accuracy	0.015625	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.017910009768442016	(cos.f64 (+.f64 x eps))
accuracy	0.7712709132796743	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	31.468000124163822	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.0078125	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	14.078735592868252	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	30.880861646770317	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	31.50467835161607	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.024101269536884032	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

195.0ms	184×	2	valid
64.0ms	68×	1	valid
2.0ms	1×	3	valid
1.0ms	3×	0	valid

Compiler

Compiled 278 to 45 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-cos: 79.0ms (36.5% of total)

ival-mult: 53.0ms (24.5% of total)

adjust: 33.0ms (15.2% of total)

ival-sub: 21.0ms (9.7% of total)

ival-add: 12.0ms (5.5% of total)

const: 10.0ms (4.6% of total)

ival-sin: 7.0ms (3.2% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series47.0ms (0.3%)

Memory

-1.2MiB live, 34.3MiB allocated

Counts

24 → 480

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x 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 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) (patch (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) (patch (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) (patch (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) (patch (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x 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 (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow eps 2)) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow eps 2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (* -1/2 (cos x)) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/24 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) (patch (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) (patch (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) (patch (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) (patch (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) (patch (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) (patch (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) (patch (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) (patch (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/24 (* (cos x) eps)))
4.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/24 (* (cos x) eps)))
4.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/24 (* (cos x) eps)))
4.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/24 (* (cos x) eps)))
4.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/24 (* (cos x) eps)))

simplify145.0ms (1%)

Memory

-9.9MiB live, 110.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 566×	`lower-fma.f64`
10 566×	`lower-fma.f32`
7 092×	`lower-*.f64`
7 092×	`lower-*.f32`
2 868×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	488	4933
1	1530	4749
2	4440	4743
0	8109	4405

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 458

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
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)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin 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))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/6 (sin x))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (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 x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/24 (* eps (cos x)))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 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 eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos 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))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -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)))
(cos (- x (* -1 eps)))
(cos (- 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)))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/24 (* eps (cos x)))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(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))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 eps)
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 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 x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(sin x)
(sin x)
(sin x)
(sin 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 x))
(cos (+ eps x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(cos x)
(cos x)
(cos x)
(cos x)
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 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))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(sin x)
(sin x)
(sin x)
(sin 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 (* -1 x)))
(cos (- 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)))
(cos x)
(cos x)
(cos x)
(cos x)
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin 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))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))

Outputs
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.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)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
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 (.f64 eps eps) #s(literal 1/24 binary64) #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))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
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(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(* 1/24 (* eps (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 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))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(* 1/24 (* eps (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(* 1/24 (* eps (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(* 1/24 (* eps (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(* 1/24 (* eps (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))

rewrite164.0ms (1.1%)

Memory

-17.0MiB live, 64.5MiB allocated

Rules

4 230×	`lower-/.f64`
4 230×	`lower-/.f32`
4 196×	`lower-*.f32`
4 174×	`lower-*.f64`
3 676×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	250
0	80	242
1	283	242
2	2267	242
0	8271	242

Stop Event

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

Counts

24 → 548

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(+.f64 #s(literal 0 binary64) eps)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 x)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (neg.f64 eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal -1/24 binary64) (.f64 (cos.f64 x) eps))) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/576 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) eps)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal -1/24 binary64) (.f64 (cos.f64 x) eps))) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64)))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal -1 binary64)) (neg.f64 eps) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal -1/24 binary64) (.f64 (cos.f64 x) eps)))) (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal -1/24 binary64) (*.f64 (cos.f64 x) eps)))))
(+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal -1 binary64)) (neg.f64 eps))
(.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps))
(.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x))
(.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (neg.f64 (*.f64 eps eps)))) eps)
(/.f64 (neg.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal -1 binary64)) (neg.f64 eps) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal -1 binary64)) (neg.f64 eps) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (.f64 #s(literal 0 binary64) (.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps) (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) eps (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 (cos.f64 x) #s(literal 1/24 binary64))) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 #s(literal 0 binary64) (.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) #s(literal 0 binary64)))

eval111.0ms (0.7%)

Memory: 18.4MiB live, 92.1MiB allocated
Compiler: Compiled 26 064 to 3 115 computations (88% saved)

prune91.0ms (0.6%)

Memory

7.5MiB live, 92.6MiB allocated

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	1 017	13	1 030
Fresh	3	0	3
Picked	3	2	5
Done	1	0	1
Total	1 024	15	1 039

Accuracy

100.0%

Counts

1 039 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	50.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
▶	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 552 to 396 computations (28.3% saved)

simplify129.0ms (0.9%)

Memory

0.4MiB live, 38.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
cost-diff	0	(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
cost-diff	0	#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
cost-diff	320	(fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
cost-diff	6592	(fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps))
cost-diff	0	(.f64 (.f64 x x) eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
cost-diff	128	(fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

13 002×	`lower-fma.f32`
12 984×	`lower-fma.f64`
5 780×	`lower-*.f32`
5 748×	`lower-*.f64`
2 366×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	656
0	114	646
1	205	646
2	548	635
3	1699	617
4	3868	614
5	5508	614
0	8024	591

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
(.f64 (.f64 x x) eps)
(*.f64 x x)
x
eps
#s(literal 1/6 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
(fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x)
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64))
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
x
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(sin.f64 x)
x

Outputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (*.f64 eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(*.f64 eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(.f64 (.f64 x x) eps)
(*.f64 x x)
x
eps
#s(literal 1/6 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps)) eps)))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps)) eps))
(fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) eps #s(literal -1 binary64)) eps)
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps)
(.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x)
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x)
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64))
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
x
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(.f64 (fma.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(fma.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps)
#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(sin.f64 x)
x

localize386.0ms (2.5%)

Memory

-7.1MiB live, 113.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x))
accuracy	0.051174462261739065	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
accuracy	0.13671875	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	1.1379450871982257	#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
accuracy	0.01171875	(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
accuracy	0.051174462261739065	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
accuracy	0.3515625	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	1.138684738146397	#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
accuracy	0.01171875	(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
accuracy	0.0859375	(.f64 (.f64 x x) eps)
accuracy	0.8971699826902428	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
accuracy	14.078735592868252	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
accuracy	0.3496159329786427	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	30.880861646770317	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	31.50467835161607	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.0078125	(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.024101269536884032	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))

Samples

267.0ms	185×	2	valid
65.0ms	68×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 451 to 71 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 264.0ms

ival-mult: 79.0ms (29.9% of total)

ival-cos: 75.0ms (28.4% of total)

adjust: 47.0ms (17.8% of total)

ival-add: 26.0ms (9.8% of total)

const: 18.0ms (6.8% of total)

ival-sub: 9.0ms (3.4% of total)

ival-sin: 7.0ms (2.6% of total)

exact: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

series54.0ms (0.4%)

Memory

-9.2MiB live, 27.8MiB allocated

Counts

24 → 516

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) (patch (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))) #<representation binary64>) () ())
#s(alt #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)) (patch #s(approx ( (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) eps) (patch (.f64 (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) (patch (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)) (patch (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) (patch (.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) (patch (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (patch (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (patch (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x) (patch (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) eps) (patch (.f64 #s(literal 1/6 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) (patch (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
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#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))) #<representation binary64>) () ())) ())
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#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))) (taylor -inf x) (#s(alt (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) (patch (.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (patch (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (patch (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x) (patch (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* (* x x) eps) 1/6) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* x x) eps) (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (+ (* 1/3840 (* eps eps)) -1/48) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (* 1/6 eps) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* (* x x) eps) 1/6) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* x x) eps) (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (+ (* 1/3840 (* eps eps)) -1/48) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (* 1/6 eps) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* (* x x) eps) 1/6) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* x x) eps) (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (+ (* 1/3840 (* eps eps)) -1/48) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (* 1/6 eps) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* (* x x) eps) 1/6) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* x x) eps) (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (+ (* 1/3840 (* eps eps)) -1/48) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (* 1/6 eps) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* (* x x) eps) 1/6) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* x x) eps) (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (+ (* 1/3840 (* eps eps)) -1/48) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (* 1/6 eps) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))

simplify135.0ms (0.9%)

Memory

13.1MiB live, 51.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 586×	`lower-fma.f64`
8 586×	`lower-fma.f32`
6 578×	`lower-*.f64`
6 578×	`lower-*.f32`
2 548×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	552	6804
1	1802	6559
2	5469	6535
0	8048	6040

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 513

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* -1 eps)
(* eps (- (* 1/4 (* eps x)) 1))
(* eps (- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1))
(* eps (- (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/48 (* eps x)))))) 1))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* -1/48 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))
(* (pow eps 4) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))
(* (pow eps 4) (- (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))) (/ 1 (pow eps 3))))
(* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2)))))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/24 (pow eps 4))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 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 eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* -1/48 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))
(* (pow eps 4) (+ (* -1 (/ (- (* -1/4 (/ x eps)) 1/6) eps)) (* -1/48 x)))
(* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (- (* 1/4 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/48 x)))
(* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))
(* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))
(* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/24 (pow eps 4))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (- (* 1/6 (pow eps 2)) 1))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* x (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* x (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* x (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 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))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin 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))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))

Outputs
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.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)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
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 (.f64 eps eps) #s(literal 1/24 binary64) #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))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (pow x 2))
(.f64 (.f64 x x) eps)
(* eps (pow x 2))
(.f64 (.f64 x x) eps)
(* eps (pow x 2))
(.f64 (.f64 x x) eps)
(* eps (pow x 2))
(.f64 (.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (* 1/4 (* eps x)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)) eps)
(* eps (- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) x)) eps #s(literal -1 binary64)) eps)
(* eps (- (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/48 (* eps x)))))) 1))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) eps #s(literal -1 binary64)) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64))) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) eps (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64))) eps (neg.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
-1/48
#s(literal -1/48 binary64)
(- (* 1/3840 (pow eps 2)) 1/48)
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(- (* 1/3840 (pow eps 2)) 1/48)
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(- (* 1/3840 (pow eps 2)) 1/48)
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* 1/6 eps)
(*.f64 #s(literal 1/6 binary64) eps)
(* 1/6 eps)
(*.f64 #s(literal 1/6 binary64) eps)
(* 1/6 eps)
(*.f64 #s(literal 1/6 binary64) eps)
(* 1/6 eps)
(*.f64 #s(literal 1/6 binary64) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* -1/2 (cos x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(* 1/6 (* eps (pow x 3)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1/6 binary64))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))

rewrite190.0ms (1.3%)

Memory

-8.2MiB live, 74.7MiB allocated

Rules

5 674×	`lower-*.f32`
5 642×	`lower-*.f64`
5 122×	`lower-fma.f32`
5 104×	`lower-fma.f64`
2 720×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	511
0	114	503
1	420	503
2	3719	497
0	9201	479

Stop Event

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

Counts

24 → 544

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
(.f64 (.f64 x x) eps)
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps))
(fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(*.f64 #s(literal 1/6 binary64) eps)
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 eps eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 eps eps))) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
(sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
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(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))) x) (*.f64 eps x))
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(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
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(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
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(+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps) #s(literal 0 binary64)))
#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))

eval119.0ms (0.8%)

Memory: 23.4MiB live, 97.1MiB allocated
Compiler: Compiled 34 534 to 3 480 computations (89.9% saved)

prune101.0ms (0.7%)

Memory

-27.1MiB live, 96.4MiB allocated

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	1 049	8	1 057
Fresh	2	6	8
Picked	2	3	5
Done	0	2	2
Total	1 053	19	1 072

Accuracy

100.0%

Counts

1 072 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
✓	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
▶	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	50.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
▶	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
▶	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))

Compiler

Compiled 631 to 460 computations (27.1% saved)

simplify169.0ms (1.1%)

Memory

15.3MiB live, 51.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
cost-diff	0	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
cost-diff	0	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
cost-diff	192	(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
cost-diff	0	#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
cost-diff	0	(.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
cost-diff	0	#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
cost-diff	0	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Rules

22 632×	`lower-fma.f32`
22 608×	`lower-fma.f64`
4 672×	`lower-*.f32`
4 646×	`lower-*.f64`
3 972×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	961
0	137	945
1	248	941
2	678	920
3	2102	904
4	4862	904
5	7709	904
0	8327	883

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))
#s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))
(.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
eps
#s(literal -1 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal -1 binary64)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)

Outputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))
#s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))
(.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
eps
#s(literal -1 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64))
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal -1 binary64)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)

localize433.0ms (2.9%)

Memory

18.2MiB live, 136.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.13671875	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
accuracy	0.3515625	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.4057436121858727	(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps))
accuracy	0.896137057305481	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
accuracy	0.051174462261739065	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
accuracy	0.13671875	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
accuracy	0.3515625	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	1.138040099840729	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
accuracy	0.01171875	(.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)
accuracy	0.8971699826902428	#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))
accuracy	14.078735592868252	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
accuracy	0	(neg.f64 x)
accuracy	0.051174462261739065	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
accuracy	1.138684738146397	#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))
accuracy	14.07986164321764	#s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))
accuracy	0.0078125	(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.024101269536884032	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	0.1328125	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))

Samples

285.0ms	176×	2	valid
76.0ms	75×	1	valid
4.0ms	2×	3	valid
2.0ms	3×	0	valid

Compiler

Compiled 552 to 87 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 310.0ms

ival-mult: 124.0ms (40% of total)

adjust: 59.0ms (19.1% of total)

ival-cos: 53.0ms (17.1% of total)

ival-add: 37.0ms (12% of total)

const: 21.0ms (6.8% of total)

ival-sin: 7.0ms (2.3% of total)

ival-sub: 6.0ms (1.9% of total)

ival-neg: 2.0ms (0.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series60.0ms (0.4%)

Memory

-2.8MiB live, 34.6MiB allocated

Counts

25 → 564

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps))) (patch #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)) (patch #s(approx (+ ( (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) eps) (patch (.f64 (neg.f64 x) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))) #<representation binary64>) () ())
#s(alt #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)) (patch #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x) (patch (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) (patch #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (patch (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) (patch (.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) (patch #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) (patch #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (patch (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) eps) (patch (.f64 #s(literal 1/6 binary64) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) (patch (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) #<representation binary64>) () ())

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* 1/2 (* eps (cos x)))) (taylor 0 eps) (#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) (taylor 0 eps) (#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps))) (patch #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps))) (patch #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) (taylor 0 eps) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps))) (patch #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))) (taylor 0 eps) (#s(alt #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps))) (patch #s(approx ( (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (neg.f64 x) eps)) (patch #s(approx (+ ( (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (neg.f64 x) eps) (patch (.f64 (neg.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (neg.f64 x) eps) (patch (.f64 (neg.f64 x) eps) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	0	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (* (neg x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) x) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* 1/3840 (* eps eps)) -1/48) (neg x) (* (+ (* (* x x) 1/6) -1) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)))
5.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (* (neg x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) x) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* 1/3840 (* eps eps)) -1/48) (neg x) (* (+ (* (* x x) 1/6) -1) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (* (neg x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) x) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* 1/3840 (* eps eps)) -1/48) (neg x) (* (+ (* (* x x) 1/6) -1) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)))
4.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (* (neg x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) x) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* 1/3840 (* eps eps)) -1/48) (neg x) (* (+ (* (* x x) 1/6) -1) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)))
4.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (* (neg x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) x) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* 1/3840 (* eps eps)) -1/48) (neg x) (* (+ (* (* x x) 1/6) -1) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)))

simplify175.0ms (1.2%)

Memory

-29.4MiB live, 58.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 076×	`lower-fma.f64`
11 076×	`lower-fma.f32`
6 690×	`lower-*.f64`
6 690×	`lower-*.f32`
4 072×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	656	7974
1	2111	7639
2	6868	7611
0	8160	7018

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 561

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* 1/3840 (pow eps 2)) 1/48)
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2)))))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* 1/24 (pow eps 3))
(* (pow eps 3) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 3) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))
(* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))
(* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* 1/24 (pow eps 3))
(* -1 (* (pow eps 3) (- (* -1/6 (/ x eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/6 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)) eps)) 1/24)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* -1 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps 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))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) 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))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin 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))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))

Outputs
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (neg.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
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(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* x (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 eps x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 eps x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 eps x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) eps (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (/.f64 eps x) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))
(.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) eps (/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) x) (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) eps (/.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 eps x) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) x) (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* 1/6 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) eps (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (/.f64 eps x) #s(literal 1/6 binary64))) x)
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) eps (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (/.f64 eps x) #s(literal 1/6 binary64))) x)
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) eps (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (/.f64 eps x) #s(literal 1/6 binary64))) x)

rewrite160.0ms (1.1%)

Memory

25.9MiB live, 63.5MiB allocated

Rules

5 532×	`lower-fma.f32`
5 508×	`lower-fma.f64`
5 314×	`lower-*.f32`
5 288×	`lower-*.f64`
2 946×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	781
0	137	767
1	523	763
2	4729	757
0	9265	731

Stop Event

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

Counts

25 → 294

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps)))
#s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))
(.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(neg.f64 x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(*.f64 #s(literal 1/6 binary64) eps)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps))

Outputs
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
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(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (-.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (-.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (-.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 3 binary64)))))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps (.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))) eps))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (neg.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
(fma.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x))
(fma.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))) eps))
(fma.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (neg.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)))
(fma.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps))))
(-.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) (neg.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)))
(+.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x))

eval93.0ms (0.6%)

Memory: 0.2MiB live, 75.1MiB allocated
Compiler: Compiled 20 579 to 2 476 computations (88% saved)

prune84.0ms (0.6%)

Memory

-14.6MiB live, 69.9MiB allocated

Pruning

21 alts after pruning (13 fresh and 8 done)

	Pruned	Kept	Total
New	866	10	876
Fresh	6	3	9
Picked	2	3	5
Done	0	5	5
Total	874	21	895

Accuracy

100.0%

Counts

895 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
✓	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	76.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
✓	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))

Compiler

Compiled 1 175 to 549 computations (53.3% saved)

regimes30.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Outputs

(*.f64 (*.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Calls

3 calls:

10.0ms	x
10.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory

-25.7MiB live, 13.6MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Outputs

(*.f64 (*.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(approx (+ (* 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))

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

Calls

3 calls:

8.0ms	x
8.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Calls

3 calls:

8.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.2%)

Memory

-26.8MiB live, 12.6MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (fma.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))

Calls

3 calls:

8.0ms	eps
8.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))

Calls

3 calls:

6.0ms	eps
6.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))

Calls

3 calls:

5.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (*.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))

Calls

3 calls:

5.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

-34.9MiB live, 8.5MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) eps))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))

Calls

3 calls:

6.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))

Calls

3 calls:

4.0ms	x
3.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) x) x)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
77.0%	1	`x`
77.0%	1	`eps`
77.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Accuracy

Total -0.5b remaining (-1.7%)

Threshold costs -0.5b (-1.7%)

Counts

2 → 1

Calls

Call 1

Inputs

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

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (*.f64 x eps))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
49.7%	1	`x`
49.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify26.0ms (0.2%)

Memory

-19.8MiB live, 20.0MiB allocated

Algorithm

1×	egg-herbie

Rules

70×	`-commutative-binary64-.f64`
14×	`+-commutative-binary64-+.f64`
14×	`sub-neg-binary64-neg.f64-+.f64--.f64`
10×	`neg-sub0-binary64--.f64-neg.f64`
10×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	674
1	196	674
2	211	674
3	224	674
4	226	674

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) eps) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) eps) x #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* (* eps eps) -1/48) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) eps) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

soundness1.1s (7.2%)

Memory

22.8MiB live, 22.8MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
11 076×	`lower-fma.f64`
11 076×	`lower-fma.f32`
10 566×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	656	7974
1	2111	7639
2	6868	7611
0	8160	7018
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	552	6804
1	1802	6559
2	5469	6535
0	8048	6040
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474
0	488	4933
1	1530	4749
2	4440	4743
0	8109	4405

Stop Event

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

Compiler

Compiled 412 to 271 computations (34.2% saved)

preprocess132.0ms (0.9%)

Memory: -9.5MiB live, 68.1MiB allocated
Compiler: Compiled 562 to 256 computations (54.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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%)

analyze68.0ms (0.4%)

sample9.5s (62.7%)

explain313.0ms (2.1%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize93.0ms (0.6%)

series6.0ms (0%)

simplify141.0ms (0.9%)

rewrite157.0ms (1%)

eval35.0ms (0.2%)

prune34.0ms (0.2%)

simplify137.0ms (0.9%)

localize311.0ms (2.1%)

series47.0ms (0.3%)

simplify145.0ms (1%)

rewrite164.0ms (1.1%)

eval111.0ms (0.7%)

prune91.0ms (0.6%)

simplify129.0ms (0.9%)

localize386.0ms (2.5%)

series54.0ms (0.4%)

simplify135.0ms (0.9%)

rewrite190.0ms (1.3%)

eval119.0ms (0.8%)

prune101.0ms (0.7%)

simplify169.0ms (1.1%)

localize433.0ms (2.9%)

series60.0ms (0.4%)

simplify175.0ms (1.2%)

rewrite160.0ms (1.1%)

eval93.0ms (0.6%)

prune84.0ms (0.6%)

regimes30.0ms (0.2%)

regimes27.0ms (0.2%)

regimes25.0ms (0.2%)

regimes23.0ms (0.2%)

regimes24.0ms (0.2%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

regimes15.0ms (0.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify26.0ms (0.2%)

soundness1.1s (7.2%)

preprocess132.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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