Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze49.0ms (0.3%)

Memory

-24.5MiB live, 52.8MiB 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 (57.2%)

Memory

68.9MiB live, 10 653.2MiB allocated

Samples

3.9s	26 218×	0	invalid
3.6s	5 678×	2	valid
568.0ms	2 460×	1	valid
14.0ms	118×	0	valid

Precisions

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

ival-cos: 2.9s (45.5% of total)

const: 822.0ms (13% of total)

adjust: 507.0ms (8% of total)

ival-<=: 472.0ms (7.5% of total)

ival-fabs: 396.0ms (6.3% of total)

ival-sub: 344.0ms (5.4% of total)

ival-<: 268.0ms (4.2% of total)

ival-mult: 251.0ms (4% of total)

ival-add: 222.0ms (3.5% of total)

ival-and: 106.0ms (1.7% of total)

exact: 47.0ms (0.7% of total)

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

Bogosity

explain211.0ms (1.2%)

Memory

19.1MiB live, 416.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
146	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	146	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	146	0
-	0	110

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	0
-	0	0	110

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	110
1	145
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

139.0ms	354×	2	valid
20.0ms	152×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-cos: 93.0ms (71.8% of total)

adjust: 27.0ms (20.9% of total)

ival-sub: 6.0ms (4.6% of total)

ival-add: 3.0ms (2.3% of total)

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

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

preprocess28.0ms (0.2%)

Memory

5.4MiB live, 43.8MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

7.9MiB live, 7.9MiB 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)

localize109.0ms (0.6%)

Memory

-2.8MiB live, 156.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.048515469444718316	(cos.f64 (+.f64 x eps))
accuracy	32.59911959297329	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

74.0ms	177×	2	valid
28.0ms	76×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-cos: 55.0ms (61.5% of total)

ival-add: 18.0ms (20.1% of total)

adjust: 13.0ms (14.5% of total)

ival-sub: 3.0ms (3.4% of total)

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

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

series5.0ms (0%)

Memory

9.1MiB live, 9.1MiB 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	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify157.0ms (0.9%)

Memory

-21.4MiB live, 217.1MiB 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)

rewrite197.0ms (1.1%)

Memory

7.6MiB live, 235.2MiB 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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eval59.0ms (0.3%)

Memory: 8.3MiB live, 132.8MiB allocated
Compiler: Compiled 6 943 to 892 computations (87.2% saved)

prune15.0ms (0.1%)

Memory

10.1MiB live, 48.5MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	295	11	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	295	12	307

Accuracy

99.8%

Counts

307 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	48.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
▶	48.3%	(-.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))))
	48.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	47.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	48.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
▶	47.5%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 303 to 240 computations (20.8% saved)

simplify559.0ms (3.1%)

Memory

-18.6MiB live, 414.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 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 (.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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	287
0	67	287
1	109	287
2	185	287
3	421	287
4	824	287
5	1677	287
6	3162	287
7	4575	287
8	5738	287
9	6178	287
10	6216	287
11	6230	287
12	6374	287
13	6557	287
14	6824	287
15	6847	287
16	6864	287
17	6864	287
0	8482	282

Stop Event

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

Calls

Call 1

Inputs
#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)
#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 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(cos.f64 eps)
eps
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(sin.f64 eps)
x
#s(literal 1 binary64)

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

localize425.0ms (2.4%)

Memory

-8.7MiB live, 697.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	1.4321584444202984	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
accuracy	32.53057514230871	(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
accuracy	0.010097509768442016	(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	0.048515469444718316	(cos.f64 (+.f64 x eps))
accuracy	0.8245631236674169	#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	32.59911959297329	(-.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	14.795953850782393	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	32.342030424925994	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	32.691956084713574	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.0234375	(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)))
accuracy	0.16015625	(.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	0.3203125	(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
accuracy	0.34765625	(.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))

Samples

255.0ms	177×	2	valid
101.0ms	76×	1	valid
12.0ms	1×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 235 to 36 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 254.0ms

ival-cos: 100.0ms (39.4% of total)

ival-mult: 50.0ms (19.7% of total)

adjust: 37.0ms (14.6% of total)

ival-sin: 21.0ms (8.3% of total)

const: 19.0ms (7.5% of total)

ival-add: 13.0ms (5.1% of total)

ival-sub: 12.0ms (4.7% of total)

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

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

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

exact: 0.0ms (0% of total)

series45.0ms (0.2%)

Memory

17.0MiB live, 95.7MiB allocated

Counts

22 → 444

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((+ (* (+ (* 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)) (- (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) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (sin eps) x) 1) (* 1/24 (* (cos x) eps)) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (sin eps))
6.0ms	x	@	-inf	((+ (* (+ (* 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)) (- (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) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (sin eps) x) 1) (* 1/24 (* (cos x) eps)) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (sin eps))
6.0ms	x	@	inf	((+ (* (+ (* 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)) (- (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) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (sin eps) x) 1) (* 1/24 (* (cos x) eps)) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (sin eps))
4.0ms	eps	@	0	((+ (* (+ (* 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)) (- (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) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (sin eps) x) 1) (* 1/24 (* (cos x) eps)) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (sin eps))
4.0ms	eps	@	inf	((+ (* (+ (* 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)) (- (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) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (sin eps) x) 1) (* 1/24 (* (cos x) eps)) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (sin eps))

simplify190.0ms (1.1%)

Memory

-30.8MiB live, 326.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	403	4293
1	1243	4255
2	3612	4170
0	8067	3873

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 436

Calls

Call 1

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

Outputs
(* -1/2 (cos x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x)))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (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 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* eps (- (* -1/2 eps) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(* eps (- (* eps (- (* 1/6 (* eps x)) 1/2)) x))
(.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)
(* eps (- (* eps (- (* eps (- (* 1/24 eps) (* -1/6 x))) 1/2)) x))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps) x) eps)
1
#s(literal 1 binary64)
(+ 1 (* eps x))
(fma.f64 eps x #s(literal 1 binary64))
(+ 1 (* eps (+ x (* -1/6 (* (pow eps 2) x)))))
(fma.f64 x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) #s(literal 1 binary64))
(+ 1 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (*.f64 eps eps) x) eps #s(literal 1 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* 1/24 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 eps (cos.f64 x)) eps) #s(literal 1/24 binary64))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps) eps)
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(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
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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))
(* -1 (* x (sin eps)))
(*.f64 (neg.f64 x) (sin.f64 eps))
(* x (- (/ (cos eps) x) (+ (sin eps) (/ 1 x))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* x (- (/ (cos eps) x) (+ (sin eps) (/ 1 x))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* x (- (/ (cos eps) x) (+ (sin eps) (/ 1 x))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* x (+ (sin eps) (/ 1 x)))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* x (+ (sin eps) (/ 1 x)))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* x (+ (sin eps) (/ 1 x)))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(* 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)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(- (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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) 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 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (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 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 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(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)
(- (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 (* x (sin eps)))
(*.f64 (neg.f64 x) (sin.f64 eps))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(fma.f64 (-.f64 (/.f64 (cos.f64 eps) x) (sin.f64 eps)) x #s(literal -1 binary64))
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* -1 (* x (- (* -1 (sin eps)) (/ 1 x))))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* -1 (* x (- (* -1 (sin eps)) (/ 1 x))))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* -1 (* x (- (* -1 (sin eps)) (/ 1 x))))
(fma.f64 (sin.f64 eps) x #s(literal 1 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(* 1/24 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(* 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)))

rewrite229.0ms (1.3%)

Memory

3.4MiB live, 318.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	229
0	67	229
1	249	229
2	1853	229
0	8595	229

Stop Event

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

Counts

22 → 361

Calls

Call 1

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

Outputs
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eval130.0ms (0.7%)

Memory: 26.2MiB live, 312.3MiB allocated
Compiler: Compiled 22 418 to 2 298 computations (89.7% saved)

prune40.0ms (0.2%)

Memory

-15.2MiB live, 106.3MiB allocated

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	818	18	836
Fresh	4	2	6
Picked	4	1	5
Done	0	1	1
Total	826	22	848

Accuracy

100.0%

Counts

848 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	48.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	81.9%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))))
▶	47.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos 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))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
▶	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))

Compiler

Compiled 867 to 598 computations (31% saved)

simplify241.0ms (1.3%)

Memory

0.8MiB live, 191.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #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 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
cost-diff	320	(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))
cost-diff	0	(-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x)
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)
cost-diff	0	#s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) 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	(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
cost-diff	0	(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x)))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	645
0	118	645
1	209	636
2	410	636
3	1149	636
4	2933	636
5	5376	636
6	7814	636
0	8008	622

Stop Event

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

Calls

Call 1

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

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

localize807.0ms (4.5%)

Memory

0.9MiB live, 607.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.014003759768442016	(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.048515469444718316	(cos.f64 (+.f64 x eps))
accuracy	0.7153412227839345	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	32.59911959297329	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.16015625	(.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
accuracy	0.359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.37728500976844204	(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))
accuracy	1.018995516274362	#s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps)
accuracy	0.01897648826221708	#s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps))
accuracy	0.171875	(.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)
accuracy	1.4321584444202984	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
accuracy	0.2429217521507228	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	32.342030424925994	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	32.691956084713574	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.01953125	(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
accuracy	0.1484375	(.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)
accuracy	0.16015625	(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
accuracy	0.36328125	(*.f64 (sin.f64 x) #s(literal 1/6 binary64))

Samples

489.0ms	176×	2	valid
120.0ms	76×	1	valid
7.0ms	2×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 452 to 73 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 531.0ms

ival-mult: 181.0ms (34.1% of total)

ival-cos: 110.0ms (20.7% of total)

adjust: 80.0ms (15.1% of total)

ival-add: 76.0ms (14.3% of total)

const: 44.0ms (8.3% of total)

ival-sub: 25.0ms (4.7% of total)

ival-sin: 11.0ms (2.1% of total)

ival-neg: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series86.0ms (0.5%)

Memory

-9.8MiB live, 26.4MiB allocated

Counts

24 → 504

Calls

Call 1

Inputs
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) (patch (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) (patch (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 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 #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ ( (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)) (patch #s(approx (- (cos eps) (+ ( (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps) (patch (.f64 (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) (patch (-.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) (patch (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) (patch (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) (patch #s(approx (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #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 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #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 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps) (patch (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (sin x) 1/6) (* (* (sin x) 1/6) eps) (* (+ (* (* eps x) 1/6) -1/2) eps) (* eps 1/6) (+ (* (+ (* (+ (* (* x x) -1/720) 1/24) (* x x)) -1/2) (* x x)) 1))
5.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (sin x) 1/6) (* (* (sin x) 1/6) eps) (* (+ (* (* eps x) 1/6) -1/2) eps) (* eps 1/6) (+ (* (+ (* (+ (* (* x x) -1/720) 1/24) (* x x)) -1/2) (* x x)) 1))
4.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (sin x) 1/6) (* (* (sin x) 1/6) eps) (* (+ (* (* eps x) 1/6) -1/2) eps) (* eps 1/6) (+ (* (+ (* (+ (* (* x x) -1/720) 1/24) (* x x)) -1/2) (* x x)) 1))
3.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (sin x) 1/6) (* (* (sin x) 1/6) eps) (* (+ (* (* eps x) 1/6) -1/2) eps) (* eps 1/6) (+ (* (+ (* (+ (* (* x x) -1/720) 1/24) (* x x)) -1/2) (* x x)) 1))
3.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (sin x) 1/6) (* (* (sin x) 1/6) eps) (* (+ (* (* eps x) 1/6) -1/2) eps) (* eps 1/6) (+ (* (+ (* (+ (* (* x x) -1/720) 1/24) (* x x)) -1/2) (* x x)) 1))

simplify265.0ms (1.5%)

Memory

15.8MiB live, 53.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	498	5952
1	1550	5872
2	4780	5855
0	8189	5426

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 498

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)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1/2 (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)))
(* -1/2 (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 x))
(* eps (- (* -1/2 eps) x))
(* eps (- (* eps (- (* 1/6 (* eps x)) 1/2)) x))
(* eps (- (* eps (- (* eps (- (* 1/24 eps) (* -1/6 x))) 1/2)) x))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* -1 x)
(- (* -1/2 eps) x)
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(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)
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* -1/2 eps)
(* eps (- (* 1/6 (* eps x)) 1/2))
(* eps (- (* 1/6 (* eps x)) 1/2))
(* eps (- (* 1/6 (* eps x)) 1/2))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 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)))))
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(* (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)))
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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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(* 1/24 (* (pow eps 3) (cos x)))
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(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
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eps
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(* 1/6 (* eps (sin x)))
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(* 1/6 (* (pow eps 2) x))
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(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
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(- (+ (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))
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(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
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(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
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(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)
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(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos eps) 1)
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(- (+ (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) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(* -1/2 (pow eps 2))
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(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
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(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
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(- (+ (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)
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(+ (* 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)))
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(- (+ (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))))
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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)))
(* 1/6 x)
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(* 1/6 (* eps x))
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(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(* -1/2 eps)
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(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))
1
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
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(- (cos (+ eps x)) (cos x))
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(- (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))
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(- (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)
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* (pow eps 2) x))
(* x (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))))
(* x (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))))
(* x (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(- (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 (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (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 (* x (sin eps)))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(* -1 (* x (- (* -1 (/ (- (cos eps) 1) x)) (* -1 (sin eps)))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow eps 2))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 (* x (+ 1 (* -1/6 (pow eps 2)))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(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)
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* (pow eps 2) x))
(* -1 (* x (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))

Outputs
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (sin.f64 x)) eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(* -1/2 (cos x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 x))
(*.f64 (neg.f64 eps) x)
(* eps (- (* -1/2 eps) x))
(*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)
(* eps (- (* eps (- (* 1/6 (* eps x)) 1/2)) x))
(.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)
(* eps (- (* eps (- (* eps (- (* 1/24 eps) (* -1/6 x))) 1/2)) x))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps) x) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* eps (+ (* -1 x) (* -1/2 eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)
(* -1 x)
(neg.f64 x)
(- (* -1/2 eps) x)
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) eps (.f64 #s(literal -1/36 binary64) x)) eps #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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 (sin.f64 x)) eps)
(* 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 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* 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)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (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 (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 (cos.f64 x))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(* eps (- (* 1/6 (* eps x)) 1/2))
(.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (* 1/6 (* eps x)) 1/2))
(.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps)
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rewrite244.0ms (1.3%)

Memory

0.6MiB live, 91.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	474
0	118	474
1	494	465
2	3998	465
0	9014	463

Stop Event

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

Counts

24 → 335

Calls

Call 1

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

Outputs
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eval148.0ms (0.8%)

Memory: 9.1MiB live, 166.3MiB allocated
Compiler: Compiled 25 020 to 2 478 computations (90.1% saved)

prune110.0ms (0.6%)

Memory

-33.4MiB live, 127.5MiB allocated

Pruning

27 alts after pruning (21 fresh and 6 done)

	Pruned	Kept	Total
New	822	11	833
Fresh	5	10	15
Picked	1	4	5
Done	0	2	2
Total	828	27	855

Accuracy

100.0%

Counts

855 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	48.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	81.9%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps (sin.f64 x))))
✓	47.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos 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))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
▶	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
✓	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
✓	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
▶	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
▶	97.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
	93.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
▶	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))

Compiler

Compiled 993 to 699 computations (29.6% saved)

simplify141.0ms (0.8%)

Memory

43.7MiB live, 234.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps)
cost-diff	0	(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
cost-diff	0	(.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))
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 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) 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 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) 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 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) 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 eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
cost-diff	320	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)))
cost-diff	576	(.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx ( 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
cost-diff	0	(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx ( 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) 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) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) 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) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	893
0	119	893
1	215	890
2	423	890
3	1093	876
4	2831	860
5	5179	860
0	8050	838

Stop Event

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

Calls

Call 1

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

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

localize438.0ms (2.4%)

Memory

-13.0MiB live, 590.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x))
accuracy	0.16015625	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps)
accuracy	0.359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	1.0794980455460914	#s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
accuracy	0.01171875	(fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
accuracy	0.01953125	(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64)))
accuracy	0.359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	1.4321438856602557	#s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)))
accuracy	0.171875	(.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)
accuracy	0.32421875	(.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)
accuracy	0.359375	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	1.4321584444202984	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
accuracy	0	(*.f64 (neg.f64 x) eps)
accuracy	0	(neg.f64 x)
accuracy	1.4321584444202984	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
accuracy	14.756649412180215	#s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps))
accuracy	0.16015625	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.3203125	(fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (*.f64 #s(literal 1/24 binary64) eps)))
accuracy	0.359375	(*.f64 #s(literal 1/24 binary64) eps)
accuracy	1.5427460321184985	#s(approx (* 1/24 (* (cos x) eps)) (*.f64 #s(literal 1/24 binary64) eps))

Samples

292.0ms	175×	2	valid
73.0ms	76×	1	valid
6.0ms	2×	3	valid
1.0ms	3×	0	valid

Compiler

Compiled 558 to 64 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 299.0ms

ival-mult: 103.0ms (34.5% of total)

ival-cos: 75.0ms (25.1% of total)

adjust: 51.0ms (17.1% of total)

ival-add: 29.0ms (9.7% of total)

const: 14.0ms (4.7% of total)

ival-sub: 11.0ms (3.7% of total)

ival-sin: 11.0ms (3.7% of total)

ival-div: 2.0ms (0.7% 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 (0.3%)

Memory

4.5MiB live, 81.9MiB allocated

Counts

28 → 624

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (neg x) eps) (neg x) (* (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) x) (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) 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) (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (* 1/24 (* (cos x) eps)) (* 1/24 eps) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/6 eps) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (* eps 1/6) (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (neg x) eps) (neg x) (* (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) x) (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) 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) (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (* 1/24 (* (cos x) eps)) (* 1/24 eps) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/6 eps) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (* eps 1/6) (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (neg x) eps) (neg x) (* (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) x) (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) 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) (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (* 1/24 (* (cos x) eps)) (* 1/24 eps) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/6 eps) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (* eps 1/6) (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (neg x) eps) (neg x) (* (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) x) (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) 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) (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (* 1/24 (* (cos x) eps)) (* 1/24 eps) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/6 eps) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (* eps 1/6) (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))
3.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (* (neg x) eps) (neg x) (* (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) x) (+ (* (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (- (cos (+ x eps)) (cos x)) (- (cos eps) (+ (* (sin eps) x) 1)) (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) 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) (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (* 1/24 (* (cos x) eps)) (* 1/24 eps) (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) (* 1/6 eps) (* (- (* (+ (* (* eps x) 1/6) -1/2) eps) x) eps) (* eps 1/6) (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)))

simplify169.0ms (0.9%)

Memory

-6.8MiB live, 193.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	495	8391
1	1641	8242
2	5052	8192
0	8738	7567

Stop Event

1×	iter limit
1×	node limit

Counts

624 → 624

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

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

rewrite212.0ms (1.2%)

Memory

7.3MiB live, 249.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	707
0	119	707
1	475	704
2	3813	704
0	9244	680

Stop Event

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

Counts

28 → 333

Calls

Call 1

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

Outputs
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eval121.0ms (0.7%)

Memory: 8.0MiB live, 204.6MiB allocated
Compiler: Compiled 27 467 to 3 129 computations (88.6% saved)

prune61.0ms (0.3%)

Memory

-5.9MiB live, 118.5MiB allocated

Pruning

29 alts after pruning (22 fresh and 7 done)

	Pruned	Kept	Total
New	1 004	10	1 014
Fresh	4	12	16
Picked	3	2	5
Done	1	5	6
Total	1 012	29	1 041

Accuracy

100.0%

Counts

1 041 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
	81.3%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps (sin.f64 x))))
✓	47.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos 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))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
✓	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
✓	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
✓	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
	97.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	97.8%	#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 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (neg.f64 eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
	76.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))

Compiler

Compiled 1 613 to 732 computations (54.6% saved)

regimes40.0ms (0.2%)

Memory

-17.5MiB live, 60.8MiB allocated

Counts

51 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))
#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 (pow.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))))

Outputs

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

Calls

3 calls:

13.0ms	x
13.0ms	eps
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.2%)

Memory

16.9MiB live, 58.0MiB allocated

Counts

46 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) #s(approx (* 1/24 (* (cos x) eps)) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

13.0ms	eps
12.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes35.0ms (0.2%)

Memory

-20.1MiB live, 58.6MiB allocated

Counts

45 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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))

Outputs

#s(approx (- (cos (+ x eps)) (cos 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))

Calls

3 calls:

12.0ms	x
11.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

16.9MiB live, 56.2MiB allocated

Counts

44 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (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))

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:

12.0ms	eps
11.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

-26.9MiB live, 54.8MiB allocated

Counts

43 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))

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

Calls

3 calls:

11.0ms	x
11.0ms	eps
10.0ms	(-.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)

regimes32.0ms (0.2%)

Memory

1.1MiB live, 40.4MiB allocated

Counts

41 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (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)))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

11.0ms	x
10.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.2%)

Memory

-1.4MiB live, 38.2MiB 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

10.0ms	x
9.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

36.9MiB live, 36.9MiB allocated

Counts

37 → 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x eps) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) x) eps (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (sin x) 1/6) eps)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (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))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) (fma.f64 #s(approx (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #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)))) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

10.0ms	x
9.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

-7.5MiB live, 34.1MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.1%)

Memory

-9.8MiB live, 28.5MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

9.0ms	eps
9.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.1%)

Memory

-12.3MiB live, 27.2MiB allocated

Counts

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

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

Calls

3 calls:

9.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

-20.9MiB live, 16.8MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

9.0ms	eps
6.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.1%)

Memory

-27.1MiB live, 15.8MiB 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) (.f64 eps eps))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 eps (fma.f64 eps #s(approx (+ ( (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6)) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal -1 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))

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

Calls

3 calls:

16.0ms	eps
5.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

16 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-17.8MiB live, 21.6MiB 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 #s(approx (+ ( (/ eps x) -1/2) (+ (* (* 1/6 eps) eps) -1)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (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)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (fma.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (* eps (+ (* eps (+ (* (+ (* -1/48 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) x) (* (* (+ (* (* eps eps) 1/24) -1/2) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* 1/6 (sin x)) (* 1/24 (* (cos x) eps))) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps #s(literal 1/6 binary64)) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) 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 (* eps eps)) 1/4) x) (* eps 1/6))) -1)) (neg.f64 eps)) x (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`eps`
97.8%	1	`x`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`eps`
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0%)

Memory

-27.1MiB live, 12.7MiB 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 (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) (+ (* (sin eps) x) 1)) (.f64 #s(approx (- ( (+ (* (* eps x) 1/6) -1/2) eps) x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) eps)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`eps`
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

2.0ms	x
1.0ms	eps
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
76.0%	1	`x`
76.0%	1	`eps`
76.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

13.7MiB live, 13.7MiB 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
47.4%	1	`x`
47.4%	1	`eps`
47.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify32.0ms (0.2%)

Memory

-12.0MiB live, 27.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	206	1093
1	275	1093
2	304	1093
3	322	1093
4	327	1093

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.5s (8%)

Memory

24.9MiB live, 24.9MiB 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
0	498	5952
1	1550	5872
2	4780	5855
0	8189	5426
0	495	8391
1	1641	8242
2	5052	8192
0	8738	7567
0	403	4293
1	1243	4255
2	3612	4170
0	8067	3873
0	76	707
0	119	707
1	475	704
2	3813	704
0	9244	680
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474

Stop Event

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

Compiler

Compiled 527 to 297 computations (43.6% saved)

preprocess185.0ms (1%)

Memory: -26.1MiB live, 93.6MiB allocated
Compiler: Compiled 962 to 368 computations (61.7% 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 (57.2%)

explain211.0ms (1.2%)

preprocess28.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize109.0ms (0.6%)

series5.0ms (0%)

simplify157.0ms (0.9%)

rewrite197.0ms (1.1%)

eval59.0ms (0.3%)

prune15.0ms (0.1%)

simplify559.0ms (3.1%)

localize425.0ms (2.4%)

series45.0ms (0.2%)

simplify190.0ms (1.1%)

rewrite229.0ms (1.3%)

eval130.0ms (0.7%)

prune40.0ms (0.2%)

simplify241.0ms (1.3%)

localize807.0ms (4.5%)

series86.0ms (0.5%)

simplify265.0ms (1.5%)

rewrite244.0ms (1.3%)

eval148.0ms (0.8%)

prune110.0ms (0.6%)

simplify141.0ms (0.8%)

localize438.0ms (2.4%)

series60.0ms (0.3%)

simplify169.0ms (0.9%)

rewrite212.0ms (1.2%)

eval121.0ms (0.7%)

prune61.0ms (0.3%)

regimes40.0ms (0.2%)

regimes36.0ms (0.2%)

regimes35.0ms (0.2%)

regimes34.0ms (0.2%)

regimes34.0ms (0.2%)

regimes32.0ms (0.2%)

regimes30.0ms (0.2%)

regimes28.0ms (0.2%)

regimes28.0ms (0.2%)

regimes27.0ms (0.1%)

regimes25.0ms (0.1%)

regimes22.0ms (0.1%)

regimes22.0ms (0.1%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes26.0ms (0.1%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify32.0ms (0.2%)

soundness1.5s (8%)

preprocess185.0ms (1%)

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