Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze49.0ms (0.3%)

Memory

-46.6MiB live, 65.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample10.3s (61.6%)

Memory

98.5MiB live, 10 745.6MiB allocated

Samples

3.9s	5 608×	2	valid
3.7s	26 485×	0	invalid
718.0ms	2 508×	1	valid
38.0ms	140×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.7s

ival-cos: 3.1s (45.9% of total)

const: 1.0s (15.4% of total)

adjust: 514.0ms (7.6% of total)

ival-fabs: 433.0ms (6.4% of total)

ival-<=: 394.0ms (5.8% of total)

ival-<: 289.0ms (4.3% of total)

ival-add: 281.0ms (4.2% of total)

ival-mult: 277.0ms (4.1% of total)

ival-sub: 267.0ms (4% of total)

ival-and: 104.0ms (1.5% of total)

exact: 40.0ms (0.6% of total)

ival-assert: 13.0ms (0.2% of total)

Bogosity

explain307.0ms (1.8%)

Memory

-18.9MiB live, 645.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
132	1	(1.7001644026362508e-154 1.941276517195146e-169)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	1	(-1117.48213597218 955.6533790069086)	-	`(cos.f64 (+.f64 x eps))`
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	133	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	132	0
-	2	122

Precision

0.9850746268656716

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	0
-	2	0	122

Precision?

0.9850746268656716

Recall?

1.0

Freqs

test

number	freq
0	122
1	134

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

163.0ms	348×	2	valid
55.0ms	158×	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: 190.0ms

ival-cos: 160.0ms (84.4% of total)

adjust: 19.0ms (10% of total)

ival-sub: 6.0ms (3.2% of total)

ival-add: 3.0ms (1.6% of total)

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

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

preprocess26.0ms (0.2%)

Memory

10.9MiB live, 49.9MiB allocated

Algorithm

1×	egg-herbie

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: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

11.7MiB live, 11.7MiB 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))

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)

localize101.0ms (0.6%)

Memory

-20.9MiB live, 149.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(cos.f64 (+.f64 x eps))
accuracy	29.599767491934628	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

83.0ms	174×	2	valid
10.0ms	79×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-cos: 67.0ms (82.6% of total)

adjust: 9.0ms (11.1% of total)

ival-sub: 3.0ms (3.7% of total)

ival-add: 2.0ms (2.5% of total)

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

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

series5.0ms (0%)

Memory

11.0MiB live, 11.0MiB 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
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))
1.0ms	eps	@	-inf	((- (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))

simplify209.0ms (1.3%)

Memory

-11.5MiB live, 268.8MiB allocated

Algorithm

1×	egg-herbie

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)

rewrite169.0ms (1%)

Memory

11.2MiB live, 290.5MiB allocated

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
#<batchref>
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eval42.0ms (0.3%)

Memory: -12.5MiB live, 102.1MiB allocated
Compiler: Compiled 6 943 to 892 computations (87.2% saved)

prune12.0ms (0.1%)

Memory

-4.4MiB live, 39.8MiB 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
✓	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.3%	(-.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))))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.8%	(.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))
▶	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.4%	#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))
▶	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 205 to 168 computations (18% saved)

simplify154.0ms (0.9%)

Memory

-2.3MiB live, 226.4MiB 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))

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	1499	304
5	2944	304
6	4146	304
7	5980	304
8	7142	304
9	7864	304
0	8038	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)

localize735.0ms (4.4%)

Memory

3.7MiB live, 373.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.125	(.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	0.24617937613559768	#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	0.3125	(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))
accuracy	0.34375	(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
accuracy	0.00390625	(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	0.00390625	(cos.f64 (+.f64 x eps))
accuracy	0.40596763005915315	#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	29.599767491934628	(-.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	0.01171875	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	13.228580083555181	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	28.973599239681477	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	29.67424825989489	#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	0.015625	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.0234375	(.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	0.1328125	(.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

474.0ms	171×	2	valid
54.0ms	79×	1	valid
12.0ms	4×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 571 to 87 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 482.0ms

ival-cos: 227.0ms (47.1% of total)

ival-mult: 167.0ms (34.7% of total)

adjust: 35.0ms (7.3% of total)

ival-sin: 20.0ms (4.2% of total)

ival-add: 11.0ms (2.3% of total)

const: 10.0ms (2.1% of total)

ival-sub: 9.0ms (1.9% of total)

exact: 1.0ms (0.2% of total)

ival-neg: 1.0ms (0.2% of total)

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

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

series74.0ms (0.4%)

Memory

-0.8MiB live, 41.5MiB 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>) () ())) ())
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#s(alt (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)) (taylor -inf x) (#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 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)) (taylor -inf x) (#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 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)) (taylor -inf x) (#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 (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (* 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
35.0ms	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)))
5.0ms	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)))
5.0ms	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	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)))

simplify212.0ms (1.3%)

Memory

24.7MiB live, 130.5MiB allocated

Algorithm

1×	egg-herbie

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)))))))))
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(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
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(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
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x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
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(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
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(- (cos eps) 1)
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(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
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(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
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(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
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eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
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(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
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(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
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(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
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(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
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(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)))
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(* (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)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(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))
(+ (* 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)))
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(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
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(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
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(+ (* 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)))
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(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
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(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
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(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 1/24 eps)
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(+ (* 1/24 eps) (* 1/6 x))
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(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
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(* 1/24 eps)
(*.f64 #s(literal 1/24 binary64) eps)
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x
(* x (+ 1 (* 1/2 (/ eps x))))
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(* x (+ 1 (* 1/2 (/ eps x))))
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(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
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(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
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(cos (+ eps x))
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(cos (+ eps x))
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x
(* x (+ 1 (/ eps x)))
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(* x (+ 1 (/ eps x)))
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(* x (+ 1 (/ eps x)))
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(cos x)
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(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
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(- (cos (+ eps x)) (cos x))
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(- (cos (+ eps x)) (cos x))
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(- (cos (+ eps x)) (cos x))
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(- (cos (+ eps x)) (cos x))
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(.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))
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))

rewrite233.0ms (1.4%)

Memory

-1.6MiB live, 204.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	250
0	80	242
1	283	242
2	2267	242
0	8270	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
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval154.0ms (0.9%)

Memory: -17.4MiB live, 160.8MiB allocated
Compiler: Compiled 26 064 to 3 115 computations (88% saved)

prune58.0ms (0.3%)

Memory

9.7MiB live, 85.7MiB allocated

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	1 016	14	1 030
Fresh	3	0	3
Picked	3	2	5
Done	0	1	1
Total	1 022	17	1 039

Accuracy

100.0%

Counts

1 039 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	99.4%	(.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)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
✓	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	99.0%	#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))
▶	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 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (.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))
	53.6%	#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 (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))))
▶	99.0%	#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 (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))))
	98.3%	#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))))
▶	79.1%	#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)))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 574 to 420 computations (26.8% saved)

simplify292.0ms (1.7%)

Memory

-9.5MiB live, 234.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
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 (.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)))
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 (.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))))
cost-diff	320	(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))
cost-diff	6272	(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))
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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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	320	(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
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	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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	832	(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	814
0	122	804
1	225	798
2	601	784
3	1913	767
4	4730	754
5	7432	754
0	8198	718

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

Outputs
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal 1/2 binary64) eps x)
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 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)) (.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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (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)) x (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (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)) x (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (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)) x (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (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)) x (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 x))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
(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))
(.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
(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 (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)) #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) (.f64 eps (fma.f64 (.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) x (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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 (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (.f64 eps (fma.f64 (.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) x (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))))
(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))
(.f64 eps (fma.f64 (.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) x (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.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)
(.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)
eps
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(.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)
(.f64 (.f64 eps x) (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 (.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))
(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps (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 #s(literal -1 binary64))))
(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))
(.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)) eps)
(.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)))
(.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) eps)
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
#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)
(.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)
(.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)
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)
(neg.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 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 binary64)

localize519.0ms (3.1%)

Memory

-26.3MiB live, 488.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.24617937613559768	#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))))
accuracy	0.3046875	(.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)))
accuracy	0.3046875	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.4849301325762683	#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)))
accuracy	0.1171875	(.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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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	0.24617937613559768	#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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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	0.3046875	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	1.0002884219072163	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
accuracy	0.08984375	(.f64 (.f64 x x) eps)
accuracy	0.486896290459176	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
accuracy	12.63763214087804	#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	0.35552714680843417	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	28.25693643066346	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	29.017441872964657	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.01953125	(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
accuracy	0.0234375	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.125	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
accuracy	0.234375	(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)

Samples

351.0ms	172×	2	valid
80.0ms	76×	1	valid
20.0ms	6×	5	exit
1.0ms	2×	0	valid

Compiler

Compiled 1 191 to 135 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 316.0ms

ival-cos: 85.0ms (26.9% of total)

ival-mult: 84.0ms (26.6% of total)

adjust: 67.0ms (21.2% of total)

ival-add: 38.0ms (12% of total)

const: 16.0ms (5.1% of total)

ival-sin: 11.0ms (3.5% of total)

ival-sub: 9.0ms (2.8% of total)

ival-div: 4.0ms (1.3% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 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

10.0MiB live, 88.1MiB allocated

Counts

24 → 516

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) (patch (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) (patch (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) (patch (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps) (patch (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 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 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 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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 #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 (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#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 (* 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 #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 (* 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 #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 (* -1/2 (pow eps 2)) (taylor 0 eps) (#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 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (taylor 0 eps) (#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 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (taylor 0 eps) (#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 (* (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 #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 1 (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow eps 2))) (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<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 #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/6 (pow x 2)) 1)) (taylor 0 eps) (#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 (* eps (- (* 1/6 (pow x 2)) 1)) (taylor 0 eps) (#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 (* eps (- (* 1/6 (pow x 2)) 1)) (taylor 0 eps) (#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 (* eps (- (* 1/6 (pow x 2)) 1)) (taylor 0 eps) (#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 (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#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 (* 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 (* (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 (* 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 (* (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 (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* eps (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (.f64 x x) eps) (patch (.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (.f64 x x) eps) (patch (.f64 (.f64 x 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 (.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))) (patch #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))) #<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 (.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))) (patch #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))) #<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 (.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))) (patch #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))) #<representation binary64>) () ())) ())
#s(alt (/ x eps) (taylor -inf x) (#s(alt (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) (patch (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (pow x 3))) (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 (* (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 (* (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 (* (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 (- (* 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)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (- (* 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)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (- (* 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)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (- (* 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)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((* (+ (/ x eps) 1/2) 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) (+ (* (* (* 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) (+ (* (* 1/6 eps) eps) -1)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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) (+ (* (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) 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) (+ (/ x eps) 1/2) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* 1/6 eps) (* eps (+ (* -1/36 (* eps eps)) 1/6)))
7.0ms	x	@	inf	((* (+ (/ x eps) 1/2) 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) (+ (* (* (* 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) (+ (* (* 1/6 eps) eps) -1)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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) (+ (* (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) 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) (+ (/ x eps) 1/2) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* 1/6 eps) (* eps (+ (* -1/36 (* eps eps)) 1/6)))
5.0ms	x	@	-inf	((* (+ (/ x eps) 1/2) 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) (+ (* (* (* 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) (+ (* (* 1/6 eps) eps) -1)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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) (+ (* (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) 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) (+ (/ x eps) 1/2) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* 1/6 eps) (* eps (+ (* -1/36 (* eps eps)) 1/6)))
5.0ms	eps	@	0	((* (+ (/ x eps) 1/2) 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) (+ (* (* (* 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) (+ (* (* 1/6 eps) eps) -1)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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) (+ (* (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) 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) (+ (/ x eps) 1/2) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* 1/6 eps) (* eps (+ (* -1/36 (* eps eps)) 1/6)))
5.0ms	eps	@	inf	((* (+ (/ x eps) 1/2) 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) (+ (* (* (* 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) (+ (* (* 1/6 eps) eps) -1)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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) (+ (* (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) 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) (+ (/ x eps) 1/2) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* 1/6 eps) (* eps (+ (* -1/36 (* eps eps)) 1/6)))

simplify190.0ms (1.1%)

Memory

6.1MiB live, 208.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	641	6656
1	2051	6409
2	6549	6384
0	8914	5892

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 501

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)))
(* 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
(- (* 1/4 (* eps x)) 1)
(- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1)
(- (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/48 (* eps x)))))) 1)
(* -1 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(+ (* -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))))))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (+ (* -1/36 (pow x 2)) (* -1/48 (* eps x)))))))) 1))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 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))))))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(* 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 (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))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* eps (+ 1/6 (* -1/36 (pow eps 2))))
(* eps (+ 1/6 (* -1/36 (pow eps 2))))
(* eps (+ 1/6 (* -1/36 (pow eps 2))))
(* 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)
(* 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 3) x))
(* (pow eps 3) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))
(* (pow eps 3) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))
(* (pow eps 3) (- (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))) (/ 1 (pow eps 3))))
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))
(* (pow eps 3) (- (+ 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 3) (- (+ 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))))))
(* -1/48 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1/36 (/ (pow x 2) eps)) (+ (* -1/48 x) (* 1/6 (/ 1 eps)))))
(* (pow eps 4) (+ (* -1/36 (/ (pow x 2) eps)) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps))))))
(* (pow eps 4) (- (+ (* -1/36 (/ (pow x 2) eps)) (+ (* -1/48 x) (+ (* 1/6 (/ (pow x 2) (pow eps 3))) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))) (/ 1 (pow eps 3))))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 4) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 4) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(- (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))))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(* 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)))
(* 1/24 (* (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))))))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/36 (pow eps 3))
(* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* 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)
(* -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 3) x))
(* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/4 x) (/ 1 eps)) eps))) eps)) (* 1/48 x))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1/6 (/ x eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 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))))
(* -1/48 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1 (/ (- (* 1/36 (pow x 2)) 1/6) eps)) (* -1/48 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6) eps)) (* -1/48 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6) eps)) (* -1/48 x)))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 4) (- (* -1 (/ (- (* 1/36 x) (* 1/4 (/ 1 eps))) eps)) 1/48))
(* (pow eps 4) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x)) eps)) 1/48))
(- (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))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(* -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))))))
(* 1/24 (* (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)))))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/36 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/36 (* 1/6 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/36 (* 1/6 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/36 (* 1/6 (/ 1 (pow eps 2))))))
(* 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)
(* -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))
(- (* 1/6 (pow eps 2)) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (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)) (* eps (* x (+ 1/4 (* -1/48 (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 (- (* 1/6 (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)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))
(+ (* 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) (+ 1/4 (* -1/48 (pow eps 2))))
(+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow 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)
(* (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)))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(* -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)))))
(* 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)))
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))
(* 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))
(* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* eps (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 1 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 (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 2) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* x (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) 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)))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 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)))
(- (* 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))
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))
(* 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))
(* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* eps (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (+ (* -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))))))
(* (pow x 2) (+ (* -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))))))
(- (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 (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow 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))
(* 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)))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 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)))))
(- (* 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))

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

rewrite167.0ms (1%)

Memory

-12.0MiB live, 187.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	563
0	122	557
1	480	553
2	4373	547
0	8793	521

Stop Event

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

Counts

24 → 431

Calls

Call 1

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

Outputs
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eval121.0ms (0.7%)

Memory: 18.1MiB live, 211.9MiB allocated
Compiler: Compiled 26 121 to 3 414 computations (86.9% saved)

prune37.0ms (0.2%)

Memory

7.9MiB live, 94.5MiB allocated

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	939	14	953
Fresh	3	6	9
Picked	3	2	5
Done	0	3	3
Total	945	25	970

Accuracy

100.0%

Counts

970 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	99.4%	(.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 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64))
✓	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
✓	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	99.0%	#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 (.f64 #s(literal -1/48 binary64) 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)) 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 (.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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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))
▶	79.0%	#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps))
	53.6%	#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 (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))))
	99.0%	#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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	99.0%	#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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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))))
	98.7%	#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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	99.0%	#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) eps)) x))))
	98.7%	#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
	98.9%	#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 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #s(literal -1 binary64))) eps)) x))))
✓	79.1%	#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)))
	79.1%	#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)))
▶	79.1%	#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 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) x)))

Compiler

Compiled 902 to 660 computations (26.8% saved)

simplify158.0ms (0.9%)

Memory

-24.4MiB live, 172.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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	512	(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 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) x)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) 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 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) x)))
cost-diff	1536	(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
cost-diff	0	(fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))
cost-diff	0	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64))
cost-diff	832	(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	968
0	130	960
1	219	947
2	415	936
3	1106	905
4	3828	875
5	7896	875
0	8001	823

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

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

localize391.0ms (2.3%)

Memory

30.7MiB live, 386.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(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	0.24617937613559768	#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	0.3046875	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.9941902931033388	#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	0.25390625	(/.f64 (/.f64 (neg.f64 eps) x) x)
accuracy	0.486896290459176	#s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) x))
accuracy	12.63763214087804	#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 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) x)))
accuracy	27.89097514436536	(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
accuracy	0.1171875	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
accuracy	0.24617937613559768	#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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
accuracy	0.5203296527328809	#s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64))
accuracy	1.0002884219072163	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
accuracy	0.1171875	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps)
accuracy	0.24617937613559768	#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps))
accuracy	1.0002884219072163	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x)))
accuracy	24.662146150656408	#s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))
accuracy	0.01953125	(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
accuracy	0.0234375	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64))
accuracy	0.125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps))))
accuracy	0.234375	(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)

Samples

249.0ms	168×	2	valid
66.0ms	79×	1	valid
18.0ms	6×	5	exit
1.0ms	3×	0	valid

Compiler

Compiled 1 019 to 124 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 248.0ms

ival-mult: 74.0ms (29.9% of total)

ival-cos: 55.0ms (22.2% of total)

adjust: 50.0ms (20.2% of total)

ival-add: 26.0ms (10.5% of total)

const: 12.0ms (4.8% of total)

ival-div: 11.0ms (4.4% of total)

ival-sin: 11.0ms (4.4% of total)

ival-sub: 6.0ms (2.4% of total)

ival-neg: 2.0ms (0.8% of total)

exact: 1.0ms (0.4% of total)

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

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

series57.0ms (0.3%)

Memory

-5.2MiB live, 32.5MiB allocated

Counts

24 → 552

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) (patch (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) (patch (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) (patch (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) (patch (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) (patch #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) #<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)) #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 (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#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 (* 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>) () ())) ())
#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>) () ())) ())
#s(alt (/ x eps) (taylor -inf x) (#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) (patch #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) (patch #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) (patch #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) (patch #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (neg.f64 eps) x) x) (patch (/.f64 (/.f64 (neg.f64 eps) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (neg.f64 eps) x) x) (patch (/.f64 (/.f64 (neg.f64 eps) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (neg.f64 eps) x) x) (patch (/.f64 (/.f64 (neg.f64 eps) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (neg.f64 eps) x) x) (patch (/.f64 (/.f64 (neg.f64 eps) x) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	((* (+ 1/2 (/ x eps)) eps) (* (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) -2) (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) (sin (* 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (* (+ (* 1/6 eps) (/ (/ (neg eps) x) x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* (+ (* (* 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) (+ 1/2 (/ x eps)) (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) (/ (/ (neg eps) x) x) (* 1/6 eps))
4.0ms	x	@	-inf	((* (+ 1/2 (/ x eps)) eps) (* (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) -2) (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) (sin (* 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (* (+ (* 1/6 eps) (/ (/ (neg eps) x) x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* (+ (* (* 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) (+ 1/2 (/ x eps)) (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) (/ (/ (neg eps) x) x) (* 1/6 eps))
4.0ms	eps	@	inf	((* (+ 1/2 (/ x eps)) eps) (* (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) -2) (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) (sin (* 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (* (+ (* 1/6 eps) (/ (/ (neg eps) x) x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* (+ (* (* 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) (+ 1/2 (/ x eps)) (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) (/ (/ (neg eps) x) x) (* 1/6 eps))
4.0ms	eps	@	-inf	((* (+ 1/2 (/ x eps)) eps) (* (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) -2) (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) (sin (* 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (* (+ (* 1/6 eps) (/ (/ (neg eps) x) x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* (+ (* (* 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) (+ 1/2 (/ x eps)) (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) (/ (/ (neg eps) x) x) (* 1/6 eps))
3.0ms	eps	@	0	((* (+ 1/2 (/ x eps)) eps) (* (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) -2) (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (* 2 x) eps)))) (sin (* 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) 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)) (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (* (+ (* 1/6 eps) (/ (/ (neg eps) x) x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* (+ (* (* 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) (+ 1/2 (/ x eps)) (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) (/ (/ (neg eps) x) x) (* 1/6 eps))

simplify142.0ms (0.8%)

Memory

10.1MiB live, 54.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	577	8210
1	1863	7880
2	6080	7818
0	8303	7195

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 549

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))))))))))
(* 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 (* 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 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(+ (* -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 (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 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2)))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 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)))
(* 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 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))))))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
-1
(- (* 1/4 (* eps x)) 1)
(- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1)
(- (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/48 (* eps x)))))) 1)
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 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))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 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)) (* 1/6 (/ x eps)))))
(* (pow eps 3) (- (+ 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 3) (- (+ 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))))))
(* 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)) (* 1/6 (/ x eps)))))
(* (pow eps 3) (- (+ 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 3) (- (+ 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))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(- (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)))
(* -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))))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(* -1/48 (* (pow eps 3) x))
(* (pow eps 3) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))
(* (pow eps 3) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))
(* (pow eps 3) (- (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))) (/ 1 (pow eps 3))))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 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))))))
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(sin (* 1/2 eps))
(sin (* 1/2 eps))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
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(* -1 (* (pow eps 3) (- (+ (* -1/6 (/ x eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
(* -1 (* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
(* -1 (* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
(* -1 (* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
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(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* -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))))))
(* -1/48 (* (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))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(* -1/48 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/4 x) (/ 1 eps)) eps))) eps)) (* 1/48 x))))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 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)
(* (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)) (* eps (* x (+ 1/4 (* -1/48 (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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(* -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))))
(- (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))
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(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* 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)))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(- (* 1/6 (pow eps 2)) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)
(- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 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)))))
(- (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 (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 1 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 (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (/ 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)))
(- (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)))
(* (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)))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* x (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
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))
(* 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 (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (+ (* -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))))))
(* (pow x 2) (+ (* -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))))))
(- (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 (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(* (pow x 2) (+ (* -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))))))
(* (pow x 2) (+ (* -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))))))
(* 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)))
(* 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)))))
(* (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)))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))
(* -1 (/ eps (pow x 2)))

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)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.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)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #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 (* 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 x)
(neg.f64 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2)))
(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))
(* -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 x)
(neg.f64 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2)))
(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 (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
(* eps (* (pow x 2) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #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)))
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(* 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 (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) x) x)
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)))
(.f64 (fma.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x #s(literal -1 binary64)) x)
(* (pow x 2) (+ (* -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))))))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) eps (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) x) x)
(* (pow x 2) (+ (* -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))))))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) eps (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) x) x)
(* 1/6 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 eps x) x) #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))
(- (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))
(* 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)))
(* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) x) eps)
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x)
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x)
(* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x)
(* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))
(.f64 (.f64 x (.f64 (.f64 eps eps) x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))
(* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)))
(.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x) 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))))))
(.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps (.f64 eps (/.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) x))) x)) x) 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))))))
(.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps (.f64 eps (/.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) x))) x)) x) 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))
(* 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)
(/ x eps)
(/.f64 x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) x)
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(fma.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(fma.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)))))
(fma.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x #s(literal -1 binary64))
(* -1 (/ eps (pow x 2)))
(/.f64 (/.f64 (neg.f64 eps) x) x)
(* -1 (/ eps (pow x 2)))
(/.f64 (/.f64 (neg.f64 eps) x) x)
(* -1 (/ eps (pow x 2)))
(/.f64 (/.f64 (neg.f64 eps) x) x)
(* -1 (/ eps (pow x 2)))
(/.f64 (/.f64 (neg.f64 eps) x) x)

rewrite152.0ms (0.9%)

Memory

-15.6MiB live, 57.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	783
0	130	776
1	458	763
2	3474	763
0	8544	715

Stop Event

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

Counts

24 → 231

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
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eval102.0ms (0.6%)

Memory: -17.2MiB live, 66.8MiB allocated
Compiler: Compiled 19 080 to 2 095 computations (89% saved)

prune33.0ms (0.2%)

Memory

7.9MiB live, 47.6MiB allocated

Pruning

24 alts after pruning (18 fresh and 6 done)

	Pruned	Kept	Total
New	775	5	780
Fresh	2	13	15
Picked	3	2	5
Done	1	4	5
Total	781	24	805

Accuracy

100.0%

Counts

805 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	99.4%	(.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))
	99.3%	(.f64 (.f64 #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)))) #s(literal -2 binary64))
✓	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
✓	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	99.0%	#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 (.f64 #s(literal -1/48 binary64) 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)) 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 (.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 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) 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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps x) #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))
✓	79.0%	#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (neg.f64 x))) eps))
	53.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	99.0%	#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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	99.0%	#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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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))))
	98.7%	#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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	99.0%	#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) eps)) x))))
	98.7%	#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
	98.9%	#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 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #s(literal -1 binary64))) eps)) x))))
	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 #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))))
	79.1%	#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)))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) x) eps))))

Compiler

Compiled 1 240 to 589 computations (52.5% saved)

regimes30.0ms (0.2%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

14.9MiB live, 14.9MiB allocated

Counts

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

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 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.2%)

Memory

-25.7MiB live, 13.9MiB 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 (* (neg eps) (sin x)) (*.f64 (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (- (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #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)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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))
#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps x) #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))
#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) 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 (* (- (* (+ (* (+ (* 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 (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) 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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) 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 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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 (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 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (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 (* (- (* (+ (* (+ (* 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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) 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 (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 (.f64 #s(literal -1/48 binary64) 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)) 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 (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)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #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))))
(.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)

regimes24.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB 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 (* (neg eps) (sin x)) (*.f64 (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (- (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #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)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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))
#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps x) #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))
#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) 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 (* (- (* (+ (* (+ (* 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 (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) 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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) 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 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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 (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 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (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 (* (- (* (+ (* (+ (* 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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) 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 (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 (.f64 #s(literal -1/48 binary64) 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)) 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 (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)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #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)) (*.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))

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)

regimes19.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB 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 (* (neg eps) (sin x)) (*.f64 (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (- (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #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)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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))
#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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps x) #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))
#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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) 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 (* (- (* (+ (* (+ (* 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 (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* (* x x) eps) 1/6) (neg eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))) 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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) 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 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (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 (fma.f64 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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 (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 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (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 (* (- (* (+ (* (+ (* 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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x)) eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))

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

6.0ms	x
6.0ms	eps
5.0ms	(-.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)

regimes17.0ms (0.1%)

Memory

-29.9MiB live, 9.7MiB allocated

Counts

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`
98.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

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

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:

4.0ms	x
4.0ms	eps
3.0ms	(-.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)

regimes10.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB 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 (* (neg eps) (sin x)) (*.f64 (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (- (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)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #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)) (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) #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)) #s(approx (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))

Calls

3 calls:

3.0ms	x
3.0ms	eps
2.0ms	(-.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)

regimes8.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

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

Outputs
#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)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.1%	1	`x`
79.1%	1	`eps`
79.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

-44.3MiB live, 5.7MiB allocated

Counts

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

Outputs

#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)))

Calls

3 calls:

12.0ms	x
2.0ms	eps
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.1%	1	`x`
79.1%	1	`eps`

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

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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
79.1%	1	`x`
79.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

4 → 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 (* (neg eps) (sin x)) (*.f64 (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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.0%	1	`x`
79.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 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)))

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
52.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
52.5%	1	`x`
52.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify25.0ms (0.2%)

Memory

20.1MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	677
1	204	677
2	218	677
3	231	677
4	235	677

Stop Event

1×

saturated

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 (.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 (.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 #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)) #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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) 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 (* (- (* (+ (* (+ (* 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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #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 #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)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (.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 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 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 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #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 #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)) #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 #s(approx (+ ( (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) #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 #s(approx (+ ( (+ (* (* eps (+ (* -1/36 (* eps eps)) 1/6)) x) (* (* (+ (* (* eps eps) -1/48) 1/4) eps) eps)) x) (* (+ (* (* 1/6 eps) eps) -1) 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 (* (- (* (+ (* (+ (* 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 (+ (* (+ (* (* (+ (* (* eps eps) -1/48) 1/4) x) eps) (+ (* (* 1/6 eps) eps) -1)) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (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)) #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 #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)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) 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 (6.5%)

Memory

-20.7MiB live, 19.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	488	4933
1	1530	4749
2	4440	4743
0	8109	4405
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	641	6656
1	2051	6409
2	6549	6384
0	8914	5892
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474
0	577	8210
1	1863	7880
2	6080	7818
0	8303	7195

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 331 to 220 computations (33.5% saved)

preprocess129.0ms (0.8%)

Memory: -6.4MiB live, 70.6MiB allocated
Compiler: Compiled 550 to 252 computations (54.2% 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%)

analyze49.0ms (0.3%)

sample10.3s (61.6%)

explain307.0ms (1.8%)

preprocess26.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize101.0ms (0.6%)

series5.0ms (0%)

simplify209.0ms (1.3%)

rewrite169.0ms (1%)

eval42.0ms (0.3%)

prune12.0ms (0.1%)

simplify154.0ms (0.9%)

localize735.0ms (4.4%)

series74.0ms (0.4%)

simplify212.0ms (1.3%)

rewrite233.0ms (1.4%)

eval154.0ms (0.9%)

prune58.0ms (0.3%)

simplify292.0ms (1.7%)

localize519.0ms (3.1%)

series60.0ms (0.4%)

simplify190.0ms (1.1%)

rewrite167.0ms (1%)

eval121.0ms (0.7%)

prune37.0ms (0.2%)

simplify158.0ms (0.9%)

localize391.0ms (2.3%)

series57.0ms (0.3%)

simplify142.0ms (0.8%)

rewrite152.0ms (0.9%)

eval102.0ms (0.6%)

prune33.0ms (0.2%)

regimes30.0ms (0.2%)

regimes28.0ms (0.2%)

regimes26.0ms (0.2%)

regimes24.0ms (0.1%)

regimes19.0ms (0.1%)

regimes17.0ms (0.1%)

regimes14.0ms (0.1%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0%)

regimes17.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify25.0ms (0.2%)

soundness1.1s (6.5%)

preprocess129.0ms (0.8%)

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