Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze74.0ms (0.4%)

Memory

-9.4MiB live, 64.0MiB 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)

sample10.8s (60.4%)

Memory

54.8MiB live, 10 682.5MiB allocated

Samples

4.4s	26 833×	0	invalid
3.7s	5 585×	2	valid
680.0ms	2 559×	1	valid
15.0ms	112×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 7.1s

ival-cos: 3.1s (44% of total)

const: 992.0ms (14% of total)

ival-add: 572.0ms (8.1% of total)

ival-fabs: 454.0ms (6.4% of total)

ival-mult: 449.0ms (6.3% of total)

ival-<=: 394.0ms (5.5% of total)

adjust: 393.0ms (5.5% of total)

ival-sub: 300.0ms (4.2% of total)

ival-<: 238.0ms (3.4% of total)

ival-and: 119.0ms (1.7% of total)

exact: 53.0ms (0.7% of total)

ival-assert: 15.0ms (0.2% of total)

Bogosity

explain241.0ms (1.4%)

Memory

2.6MiB live, 415.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
142	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	-	`(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	142	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	142	0
-	0	114

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	142	0	0
-	0	0	114

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	114
1	140
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

156.0ms	338×	2	valid
22.0ms	166×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 152.0ms

ival-cos: 121.0ms (79.5% of total)

adjust: 21.0ms (13.8% of total)

ival-sub: 7.0ms (4.6% of total)

ival-add: 3.0ms (2% of total)

ival-true: 1.0ms (0.7% of total)

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

preprocess29.0ms (0.2%)

Memory

2.7MiB live, 41.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0%)

Memory

13.0MiB live, 13.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize90.0ms (0.5%)

Memory

-0.8MiB live, 160.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.09641390224715446	(cos.f64 (+.f64 x eps))
accuracy	31.621206341088644	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

70.0ms	169×	2	valid
12.0ms	83×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-cos: 52.0ms (74.5% of total)

adjust: 13.0ms (18.6% of total)

ival-sub: 3.0ms (4.3% of total)

ival-add: 2.0ms (2.9% of total)

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

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

series19.0ms (0.1%)

Memory

-31.4MiB live, 7.4MiB 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
15.0ms	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))

simplify187.0ms (1%)

Memory

29.1MiB live, 190.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite204.0ms (1.1%)

Memory

-1.9MiB live, 275.2MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

Outputs
#<batchref>
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eval43.0ms (0.2%)

Memory: -5.2MiB live, 102.7MiB allocated
Compiler: Compiled 6 943 to 892 computations (87.2% saved)

prune16.0ms (0.1%)

Memory

-2.2MiB live, 45.9MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

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

Accuracy

99.8%

Counts

307 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	49.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	49.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.6%	#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))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 193 to 164 computations (15% saved)

simplify381.0ms (2.1%)

Memory

1.5MiB live, 316.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

22 564×	`lower-fma.f32`
22 554×	`lower-fma.f64`
4 770×	`lower-*.f32`
4 750×	`lower-*.f64`
2 628×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	261
0	77	251
1	137	251
2	279	247
3	562	247
4	1154	247
5	1984	247
6	2580	247
7	3300	247
8	4070	247
9	5553	247
10	6297	247
11	6442	247
12	6544	247
13	6667	247
14	6897	247
15	7382	247
16	7641	247
17	7784	247
18	7790	247
19	7796	247
20	7800	247
0	8641	243

Stop Event

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

Calls

Call 1

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

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

localize339.0ms (1.9%)

Memory

6.0MiB live, 623.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.015625	(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))
accuracy	0.11364604524814653	#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))
accuracy	0.15625	(.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)
accuracy	0.00390625	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
accuracy	0.09641390224715446	(cos.f64 (+.f64 x eps))
accuracy	0.7920928110550576	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	31.621206341088644	(-.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	14.01644333858418	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	31.29947436383332	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	31.65397889093498	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.07817158619651096	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.16015625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

247.0ms	174×	2	valid
54.0ms	80×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 223 to 44 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-cos: 80.0ms (35% of total)

ival-mult: 59.0ms (25.8% of total)

adjust: 54.0ms (23.6% of total)

ival-add: 12.0ms (5.2% of total)

const: 8.0ms (3.5% of total)

ival-sub: 7.0ms (3.1% of total)

ival-sin: 7.0ms (3.1% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series86.0ms (0.5%)

Memory

-24.8MiB live, 54.4MiB allocated

Counts

23 → 444

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
42.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* eps eps) 1/6) -1) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (* (cos x) -1/2) eps))
6.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* eps eps) 1/6) -1) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (* (cos x) -1/2) eps))
4.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* eps eps) 1/6) -1) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (* (cos x) -1/2) eps))
4.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* eps eps) 1/6) -1) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (* (cos x) -1/2) eps))
3.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* eps eps) 1/6) -1) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (* (cos x) -1/2) eps))

simplify498.0ms (2.8%)

Memory

7.1MiB live, 200.8MiB allocated

Algorithm

1×	egg-herbie

Rules

14 402×	`lower-fma.f64`
14 402×	`lower-fma.f32`
6 380×	`lower-*.f64`
6 380×	`lower-*.f32`
4 428×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	409	4100
1	1246	3915
2	3477	3853
0	8040	3614

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 422

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* -1 (* 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 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1 (* 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)) (* 1/6 (* eps (sin x)))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (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)
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (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))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos x)
(cos x)
(cos x)
(cos x)
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))

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

rewrite245.0ms (1.4%)

Memory

14.8MiB live, 173.4MiB allocated

Rules

5 906×	`lower-fma.f32`
5 896×	`lower-fma.f64`
5 114×	`lower-*.f32`
5 094×	`lower-*.f64`
4 708×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	207
0	77	199
1	271	199
2	2078	199
0	9939	199

Stop Event

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

Counts

23 → 622

Calls

Call 1

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

Outputs
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eval328.0ms (1.8%)

Memory: 9.6MiB live, 284.3MiB allocated
Compiler: Compiled 25 953 to 3 158 computations (87.8% saved)

prune94.0ms (0.5%)

Memory

-18.7MiB live, 105.2MiB allocated

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1 039	17	1 056
Fresh	2	1	3
Picked	2	3	5
Done	1	0	1
Total	1 044	21	1 065

Accuracy

100.0%

Counts

1 065 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
▶	49.2%	(-.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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
	84.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
▶	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
✓	99.6%	#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))
✓	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
▶	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
▶	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 619 to 482 computations (22.1% saved)

simplify474.0ms (2.7%)

Memory

26.8MiB live, 259.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff	512	(fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff	6592	(fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps)))
cost-diff	0	#s(approx (cos 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) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
cost-diff	0	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
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 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))

Rules

22 224×	`lower-fma.f32`
22 212×	`lower-fma.f64`
4 506×	`lower-*.f32`
4 484×	`lower-*.f64`
2 316×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	369
0	89	365
1	165	365
2	326	365
3	695	361
4	1218	358
5	2189	349
6	4065	349
7	5627	349
8	6834	349
9	7097	349
10	7177	349
11	7215	349
12	7603	349
13	7923	349
14	7923	349
15	7923	349
16	7923	349
17	7923	349
18	7923	349
0	8385	337

Stop Event

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

Calls

Call 1

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

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

localize393.0ms (2.2%)

Memory

-19.3MiB live, 505.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
accuracy	0.109375	(.f64 (.f64 eps x) eps)
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy	1.4629763819639932	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0	(+.f64 x eps)
accuracy	0.09641390224715446	(cos.f64 (+.f64 x eps))
accuracy	1.5174181519701704	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.621206341088644	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)
accuracy	0.01171875	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
accuracy	0.9760156903900803	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x))
accuracy	14.01644333858418	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
accuracy	0.22116033331690615	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	31.29947436383332	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	31.65397889093498	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.0078125	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.015625	(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))
accuracy	0.015625	(.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))

Samples

295.0ms	174×	2	valid
55.0ms	80×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 257 to 48 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 285.0ms

ival-cos: 108.0ms (37.9% of total)

ival-mult: 77.0ms (27% of total)

adjust: 41.0ms (14.4% of total)

ival-sub: 27.0ms (9.5% of total)

ival-add: 20.0ms (7% of total)

const: 4.0ms (1.4% of total)

ival-sin: 4.0ms (1.4% of total)

ival-pow: 3.0ms (1.1% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series50.0ms (0.3%)

Memory

-16.7MiB live, 65.4MiB allocated

Counts

23 → 492

Calls

Call 1

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

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) 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)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) 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)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 eps) (#s(alt (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow eps 2)) 1) (taylor 0 eps) (#s(alt (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow eps 2)) 1) (taylor 0 eps) (#s(alt (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow eps 2)) 1) (taylor 0 eps) (#s(alt (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow eps 2)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow eps 2))) (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (taylor 0 eps) (#s(alt #s(approx (cos eps) #s(literal 1 binary64)) (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (patch #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (patch #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (patch #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (patch #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) (patch (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) (patch (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) (patch (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) (patch (.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (pow x 3))) (taylor -inf x) (#s(alt (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) (patch (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) (patch (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) (patch (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) (patch (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 eps x) eps) (patch (.f64 (.f64 eps x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 eps x) eps) (patch (.f64 (.f64 eps x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 eps x) eps) (patch (.f64 (.f64 eps x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) x) (taylor -inf x) (#s(alt (.f64 (.f64 eps x) eps) (patch (.f64 (.f64 eps x) eps) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify161.0ms (0.9%)

Memory

-5.6MiB live, 155.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 680×	`lower-fma.f64`
13 680×	`lower-fma.f32`
7 110×	`lower-*.f64`
7 110×	`lower-*.f32`
4 148×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	383	4982
1	1139	4840
2	3499	4742
0	8294	4491

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 486

Calls

Call 1

Inputs
(* -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)) (* 1/6 (* eps (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 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(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)
(* eps (- (* 1/4 (* eps x)) 1))
(* eps (- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1))
(* eps (- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (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)) (* 1/6 (* eps (sin x)))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(- (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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* 1/4 (/ x eps))))
(* (pow eps 3) (- (+ 1/6 (* 1/4 (/ x eps))) (/ 1 (pow eps 2))))
(* (pow eps 3) (- (+ 1/6 (* 1/4 (/ x eps))) (/ 1 (pow eps 2))))
(* 1/6 (* (pow eps 3) x))
(* (pow eps 3) (- (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin 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))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* 1/6 (pow eps 3))
(* -1 (* (pow eps 3) (- (* -1/4 (/ x eps)) 1/6)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/4 x) (/ 1 eps)) eps)) 1/6)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/4 x) (/ 1 eps)) eps)) 1/6)))
(* 1/6 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 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))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 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)))))))))
(* -1 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 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)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (* 1/6 (pow eps 3)) eps)
(- (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))) eps)
(- (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))) eps)
(- (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))) eps)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/6 (pow eps 3)) eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))) eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))) eps)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(- (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)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(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)
(* 1/4 (* (pow eps 2) x))
(* x (- (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) (/ eps x)))
(* x (- (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) (/ eps x)))
(* x (- (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) (/ eps x)))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) (/ eps x)))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2)))) (/ eps x)))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2)))) (/ eps x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin 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))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin 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))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 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 (- 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)
(* 1/4 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (- (* 1/6 (pow eps 3)) eps) x)) (* -1/4 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/6 (pow eps 3)) eps) x)) (* -1/4 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/6 (pow eps 3)) eps) x)) (* -1/4 (pow eps 2)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) (/ eps x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 3)) eps)) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 3)) eps)) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (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 (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)
(* (pow eps 2) x)

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

rewrite157.0ms (0.9%)

Memory

23.7MiB live, 182.1MiB allocated

Rules

6 508×	`lower-fma.f32`
6 496×	`lower-fma.f64`
4 714×	`lower-*.f32`
4 692×	`lower-*.f64`
3 312×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	313
0	89	309
1	328	309
2	2232	309
0	8485	305

Stop Event

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

Counts

23 → 399

Calls

Call 1

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

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eval108.0ms (0.6%)

Memory: 17.2MiB live, 175.1MiB allocated
Compiler: Compiled 19 957 to 2 341 computations (88.3% saved)

prune34.0ms (0.2%)

Memory

4.2MiB live, 80.1MiB allocated

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	877	8	885
Fresh	3	10	13
Picked	3	2	5
Done	0	3	3
Total	883	23	906

Accuracy

100.0%

Counts

906 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	49.2%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
	84.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
✓	99.6%	#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))
✓	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
▶	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
▶	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
✓	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 588 to 470 computations (20.1% saved)

simplify198.0ms (1.1%)

Memory

-16.7MiB live, 232.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps))
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff	64	(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
cost-diff	0	(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
cost-diff	0	(neg.f64 (sin.f64 x))
cost-diff	0	#s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
cost-diff	320	(fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))

Rules

17 412×	`lower-fma.f32`
17 396×	`lower-fma.f64`
3 474×	`lower-*.f32`
3 446×	`lower-*.f64`
2 978×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	642
0	110	635
1	202	635
2	396	635
3	1005	620
4	2266	610
5	4487	604
6	6655	604
0	8029	573

Stop Event

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

Calls

Call 1

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

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

localize314.0ms (1.8%)

Memory

8.9MiB live, 287.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps))
accuracy	0.015625	(.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
accuracy	1.5047974438170315	#s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy	0.15625	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.29525375976844204	(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps))
accuracy	0.9699960560615559	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.00390625	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
accuracy	0.0078125	(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)
accuracy	0.9760156903900803	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))
accuracy	14.01644333858418	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
accuracy	0	(neg.f64 x)
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
accuracy	1.4629763819639932	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))
accuracy	14.110427164139269	#s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))
accuracy	0.015625	(fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps))
accuracy	0.015625	(.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)
accuracy	0.11364604524814653	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
accuracy	0.19858378117071238	#s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))

Samples

195.0ms	167×	2	valid
66.0ms	85×	1	valid
2.0ms	4×	0	valid

Compiler

Compiled 390 to 58 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-mult: 65.0ms (31.5% of total)

ival-cos: 49.0ms (23.8% of total)

adjust: 40.0ms (19.4% of total)

ival-add: 25.0ms (12.1% of total)

const: 11.0ms (5.3% of total)

ival-sin: 5.0ms (2.4% of total)

ival-neg: 4.0ms (1.9% of total)

ival-sub: 3.0ms (1.5% of total)

ival-pow: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series47.0ms (0.3%)

Memory

-10.4MiB live, 27.8MiB allocated

Counts

25 → 552

Calls

Call 1

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

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

Calls

6 calls:

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

simplify164.0ms (0.9%)

Memory

-12.3MiB live, 62.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 448×	`lower-fma.f64`
14 448×	`lower-fma.f32`
7 728×	`lower-*.f64`
7 728×	`lower-*.f32`
3 918×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	402	6687
1	1247	6493
2	3811	6415
0	8728	6043

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

Inputs
(* -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)) (* 1/6 (* eps (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 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (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)) (* 1/6 (* eps (sin x)))))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 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 (* -1/36 (* eps x)))))
(- (* 1/6 (pow x 2)) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* 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)) (* 1/6 (* eps (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)) (* 1/6 (* eps (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 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) x))
(* (pow eps 3) (- (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* 1/6 (* (pow eps 3) (sin x)))
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(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
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(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/6 (* (pow eps 3) (sin x)))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
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(* -1 (* eps x))
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(* -1 (* eps x))
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(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
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(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
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(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
-1
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(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
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(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
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(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
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(- (cos eps) 1)
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(* x (- (* 1/6 (pow eps 2)) 1))
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(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
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(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
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(* -1/2 eps)
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(* -1/2 (pow eps 2))
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(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos 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))
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(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
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(* -1/2 (* (pow eps 2) (cos x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
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(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
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(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
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(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
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(- (cos (- eps (* -1 x))) (cos x))
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(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* 1/4 (* (pow eps 2) (pow x 2)))
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 3)) eps)) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 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))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin 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))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))

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

rewrite167.0ms (0.9%)

Memory

16.1MiB live, 58.6MiB allocated

Rules

4 760×	`lower-*.f32`
4 732×	`lower-*.f64`
4 426×	`lower-fma.f32`
4 410×	`lower-fma.f64`
3 454×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	539
0	110	532
1	392	532
2	2782	532
0	8296	517

Stop Event

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

Counts

25 → 349

Calls

Call 1

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

Outputs
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eval107.0ms (0.6%)

Memory: 5.8MiB live, 80.9MiB allocated
Compiler: Compiled 25 638 to 2 505 computations (90.2% saved)

prune44.0ms (0.2%)

Memory

-34.8MiB live, 55.0MiB allocated

Pruning

27 alts after pruning (20 fresh and 7 done)

	Pruned	Kept	Total
New	889	12	901
Fresh	5	8	13
Picked	3	2	5
Done	0	5	5
Total	897	27	924

Accuracy

100.0%

Counts

924 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	49.2%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
	84.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))) eps))
✓	99.6%	#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))
✓	78.1%	#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 (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	49.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
✓	77.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
✓	77.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 1 242 to 613 computations (50.6% saved)

regimes33.0ms (0.2%)

Memory

16.8MiB live, 16.8MiB 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.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 (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)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.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 (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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))

Calls

3 calls:

11.0ms	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)

regimes31.0ms (0.2%)

Memory

-23.9MiB live, 15.5MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x)))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))

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

Calls

3 calls:

9.0ms	x
8.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

-27.6MiB live, 12.0MiB 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 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 eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))) (*.f64 x x) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (*.f64 x x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (*.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))

Calls

3 calls:

8.0ms	eps
7.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (*.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #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
98.6%	1	`x`
98.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

6.0ms	eps
5.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.2%	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)

regimes14.0ms (0.1%)

Memory

-30.8MiB live, 8.8MiB 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) eps) x (.f64 (neg.f64 eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))

Outputs

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.0MiB live, 4.0MiB 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
49.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
49.1%	1	`x`
49.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify27.0ms (0.2%)

Memory

-21.3MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Rules

68×	`-commutative-binary64-.f64`
12×	`+-commutative-binary64-+.f64`
12×	`sub-neg-binary64-neg.f64-+.f64--.f64`
10×	`neg-sub0-binary64--.f64-neg.f64`
10×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	600
1	181	600
2	195	600
3	207	600
4	208	600

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64))) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 (.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))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (neg.f64 (sin.f64 x))) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (.f64 x x) (.f64 #s(literal -1/6 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (.f64 x x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (+ (* 1/6 (* eps eps)) -1) (sin x)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps (.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 #s(approx (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (* 1/4 eps)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (+ (* (pow eps 3) 1/6) (neg eps))) (neg.f64 eps)) x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

soundness1.3s (7.4%)

Memory

25.0MiB live, 25.0MiB allocated

Rules

14 448×	`lower-fma.f64`
14 448×	`lower-fma.f32`
14 402×	`lower-fma.f64`
14 402×	`lower-fma.f32`
14 158×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	207
0	77	199
1	271	199
2	2078	199
0	9939	199
0	409	4100
1	1246	3915
2	3477	3853
0	8040	3614
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	402	6687
1	1247	6493
2	3811	6415
0	8728	6043
0	383	4982
1	1139	4840
2	3499	4742
0	8294	4491
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×	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

Compiler

Compiled 438 to 296 computations (32.4% saved)

preprocess161.0ms (0.9%)

Memory: -11.7MiB live, 66.3MiB allocated
Compiler: Compiled 592 to 250 computations (57.8% 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%)

analyze74.0ms (0.4%)

sample10.8s (60.4%)

explain241.0ms (1.4%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0%)

localize90.0ms (0.5%)

series19.0ms (0.1%)

simplify187.0ms (1%)

rewrite204.0ms (1.1%)

eval43.0ms (0.2%)

prune16.0ms (0.1%)

simplify381.0ms (2.1%)

localize339.0ms (1.9%)

series86.0ms (0.5%)

simplify498.0ms (2.8%)

rewrite245.0ms (1.4%)

eval328.0ms (1.8%)

prune94.0ms (0.5%)

simplify474.0ms (2.7%)

localize393.0ms (2.2%)

series50.0ms (0.3%)

simplify161.0ms (0.9%)

rewrite157.0ms (0.9%)

eval108.0ms (0.6%)

prune34.0ms (0.2%)

simplify198.0ms (1.1%)

localize314.0ms (1.8%)

series47.0ms (0.3%)

simplify164.0ms (0.9%)

rewrite167.0ms (0.9%)

eval107.0ms (0.6%)

prune44.0ms (0.2%)

regimes33.0ms (0.2%)

regimes32.0ms (0.2%)

regimes31.0ms (0.2%)

regimes25.0ms (0.1%)

regimes23.0ms (0.1%)

regimes22.0ms (0.1%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify27.0ms (0.2%)

soundness1.3s (7.4%)

preprocess161.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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