Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze74.0ms (0.4%)

Memory

-31.4MiB live, 49.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample10.3s (59.7%)

Memory

130.8MiB live, 10 919.8MiB allocated

Samples

4.6s	26 362×	0	invalid
3.4s	5 746×	2	valid
486.0ms	2 375×	1	valid
20.0ms	135×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.9s

ival-cos: 3.0s (44.3% of total)

const: 1.3s (18.3% of total)

ival-add: 388.0ms (5.6% of total)

ival-sub: 378.0ms (5.5% of total)

adjust: 377.0ms (5.5% of total)

ival-mult: 370.0ms (5.4% of total)

ival-<=: 346.0ms (5% of total)

ival-<: 279.0ms (4.1% of total)

ival-fabs: 262.0ms (3.8% of total)

ival-and: 103.0ms (1.5% of total)

exact: 49.0ms (0.7% of total)

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

Bogosity

explain291.0ms (1.7%)

Memory

0.0MiB live, 432.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
129	2	(4.0343314088631194e-159 8.658876478097162e-165)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	131	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	130	0
-	2	124

Precision

0.9848484848484849

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	0
-	2	0	124

Precision?

0.9848484848484849

Recall?

1.0

Freqs

test

number	freq
0	124
1	131
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

161.0ms	352×	2	valid
67.0ms	150×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 186.0ms

ival-cos: 125.0ms (67% of total)

ival-add: 34.0ms (18.2% of total)

adjust: 20.0ms (10.7% of total)

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

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

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

preprocess27.0ms (0.2%)

Memory

16.1MiB live, 54.4MiB 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 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

-23.8MiB live, 14.1MiB 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)

localize105.0ms (0.6%)

Memory

13.7MiB live, 240.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.06652107453094697	(cos.f64 (+.f64 x eps))
accuracy	29.10413501852235	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

79.0ms	176×	2	valid
11.0ms	75×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-cos: 56.0ms (78.1% of total)

adjust: 10.0ms (14% of total)

ival-sub: 3.0ms (4.2% of total)

ival-add: 2.0ms (2.8% of total)

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

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

series5.0ms (0%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify149.0ms (0.9%)

Memory

-2.2MiB live, 268.1MiB 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 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 #s(literal 1/24 binary64) eps))) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) 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 (fma.f64 eps (.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (neg.f64 eps) (sin.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 eps (.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) eps))
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)
(-.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (*.f64 #s(literal 1/2 binary64) x) x)) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #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 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (neg.f64 x) (sin.f64 eps)))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (.f64 (sin.f64 eps) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
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)

rewrite188.0ms (1.1%)

Memory

-27.2MiB live, 372.8MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval35.0ms (0.2%)

Memory: 2.7MiB live, 119.0MiB allocated
Compiler: Compiled 8 008 to 873 computations (89.1% saved)

prune49.0ms (0.3%)

Memory

4.2MiB live, 161.2MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	297	9	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Accuracy

99.9%

Counts

307 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.5%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
✓	54.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	53.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	53.4%	(-.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))
▶	53.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	80.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 257 to 168 computations (34.6% saved)

simplify393.0ms (2.3%)

Memory

15.0MiB live, 251.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
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	(.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 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 #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)) 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 #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)) 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)

localize401.0ms (2.3%)

Memory

7.0MiB live, 402.2MiB 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	0.01953125	(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	0.078125	(.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	0.2838621846486539	#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	0.01171875	(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	0.06652107453094697	(cos.f64 (+.f64 x eps))
accuracy	0.9035845240140984	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	29.10413501852235	(-.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	0.00390625	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	12.430213897098842	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	28.81167318931255	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	29.07688848972731	#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	0.0078125	(.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	0.08203125	(.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))))
accuracy	0.1019392681796303	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))

Samples

256.0ms	177×	2	valid
71.0ms	75×	1	valid
5.0ms	2×	3	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: 286.0ms

ival-cos: 82.0ms (28.7% of total)

ival-mult: 69.0ms (24.2% of total)

ival-sin: 55.0ms (19.3% of total)

adjust: 36.0ms (12.6% of total)

ival-sub: 25.0ms (8.8% of total)

ival-add: 11.0ms (3.9% of total)

const: 7.0ms (2.5% 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)

series120.0ms (0.7%)

Memory

-32.9MiB live, 52.9MiB allocated

Counts

22 → 432

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 (.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 (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.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.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>) () ())) ())
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#s(alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) (taylor -inf x) (#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 (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#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 (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#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>) () ())) ())
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#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (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>) () ())) ())
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#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (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 (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#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 (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#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 -inf x) (#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 -inf x) (#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 -inf x) (#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 -inf x) (#s(alt (.f64 (neg.f64 eps) (sin.f64 x)) (patch (.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#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))) (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))) (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))) (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 (* 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))) (* (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 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* 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
64.0ms	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) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (* (* (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) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (* (* (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) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (* (* (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) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (* (* (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) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (* (* (cos x) -1/2) eps))

simplify287.0ms (1.7%)

Memory

23.3MiB live, 179.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 432×	`lower-fma.f64`
14 432×	`lower-fma.f32`
6 358×	`lower-*.f64`
6 358×	`lower-*.f32`
4 464×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	413	4038
1	1254	3853
2	3494	3791
0	8044	3553

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 410

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 (* 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 (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))))))
(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))))
(* -1/2 (* 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 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 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)))))
(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))
(* -1/2 (* 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 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)))))
(* 1/6 (* (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))))
(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))
(* -1/2 (* 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 (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) (* 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
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* -1/2 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))
(* 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))) (* (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 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (* 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))
(* 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))) (* (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 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (* 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))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #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 #s(literal 1/6 binary64) eps) eps #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 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #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))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 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 #s(literal 1/6 binary64) eps) eps #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 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #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 (neg.f64 eps) (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (sin.f64 x)) eps (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 x)))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 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 #s(literal 1/6 binary64) eps) eps #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 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (sin.f64 x) (.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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 eps (.f64 #s(literal -1/8 binary64) eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* -1/2 (* 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 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
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(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #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 #s(literal 1/6 binary64) eps) eps #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 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/24 binary64))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))
(* -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)

rewrite240.0ms (1.4%)

Memory

13.8MiB live, 206.0MiB 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	206
0	77	198
1	271	198
2	2078	198
0	9939	198

Stop Event

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

Counts

22 → 596

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

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

eval214.0ms (1.2%)

Memory: 4.4MiB live, 190.8MiB allocated
Compiler: Compiled 27 763 to 2 444 computations (91.2% saved)

prune330.0ms (1.9%)

Memory

-36.5MiB live, 259.0MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	998	20	1 018
Fresh	3	1	4
Picked	2	3	5
Done	0	1	1
Total	1 003	25	1 028

Accuracy

100.0%

Counts

1 028 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.5%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
✓	54.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	35.2%	(.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 (.f64 (.f64 eps eps) eps) (*.f64 eps 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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	85.4%	#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)))
✓	53.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	53.3%	#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)))
▶	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.4%	#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))
✓	99.4%	#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))
✓	80.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
▶	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
	98.3%	#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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	97.9%	#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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.8%	#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 x #s(literal 1/4 binary64) (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	54.5%	#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))
▶	97.9%	#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 776 to 465 computations (40.1% saved)

simplify150.0ms (0.9%)

Memory

10.4MiB live, 163.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -1/2 binary64) eps)
cost-diff	0	(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
cost-diff	0	(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
cost-diff	0	#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))
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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff	320	(fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff	640	(fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps))
cost-diff	0	#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
cost-diff	0	(neg.f64 eps)
cost-diff	0	(.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (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	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))

Rules

12 178×	`lower-fma.f32`
12 166×	`lower-fma.f64`
4 536×	`lower-*.f32`
4 508×	`lower-*.f64`
1 638×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	399
0	102	393
1	180	393
2	383	383
3	893	374
4	2061	371
5	3159	371
6	4635	371
7	6970	371
0	8116	354

Stop Event

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

Calls

Call 1

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

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

localize633.0ms (3.7%)

Memory

-3.6MiB live, 496.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
accuracy	0.08984375	(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
accuracy	0.3128283084426344	#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))
accuracy	0.0859375	(.f64 (.f64 eps x) eps)
accuracy	0.2838621846486539	#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy	0.34375	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	1.2767893787002682	#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0.00390625	(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
accuracy	0.00390625	(.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
accuracy	1.0089719187545159	#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
accuracy	12.430213897098842	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
accuracy	0.3584105381423651	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	28.81167318931255	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	29.07688848972731	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
accuracy	0.08203125	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.1019392681796303	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Samples

400.0ms	177×	2	valid
53.0ms	75×	1	valid
6.0ms	2×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 271 to 65 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 411.0ms

ival-mult: 145.0ms (35.3% of total)

adjust: 107.0ms (26% of total)

ival-cos: 84.0ms (20.4% of total)

ival-neg: 30.0ms (7.3% of total)

ival-add: 19.0ms (4.6% of total)

ival-sin: 12.0ms (2.9% of total)

const: 7.0ms (1.7% of total)

ival-sub: 6.0ms (1.5% of total)

exact: 1.0ms (0.2% of total)

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

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

series46.0ms (0.3%)

Memory

11.2MiB live, 92.5MiB allocated

Counts

23 → 456

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #<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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) (patch (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #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)) (patch #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)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) eps) (patch (.f64 #s(literal -1/2 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) eps) (patch (.f64 #s(literal 1/6 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps x) eps) (patch (.f64 (.f64 eps 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 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #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 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) (patch (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* (pow eps 2) (pow x 2))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) 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)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)) (patch #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)) #<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 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)) (patch #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)) #<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 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)) (patch #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)) #<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 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)) (patch #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)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (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 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (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 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (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 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (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>) () ())) ())
#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
10.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (* (+ (* (* x x) -1/6) 1) x) (* 1/6 eps) (* (* eps x) eps) (cos x))
6.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (* (+ (* (* x x) -1/6) 1) x) (* 1/6 eps) (* (* eps x) eps) (cos x))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (* (+ (* (* x x) -1/6) 1) x) (* 1/6 eps) (* (* eps x) eps) (cos x))
4.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (* (+ (* (* x x) -1/6) 1) x) (* 1/6 eps) (* (* eps x) eps) (cos x))
3.0ms	eps	@	0	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) (* -1/2 eps) (* (+ (* (* x x) -1/6) 1) x) (* 1/6 eps) (* (* eps x) eps) (cos x))

simplify162.0ms (0.9%)

Memory

-19.8MiB live, 251.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 448×	`lower-fma.f64`
12 448×	`lower-fma.f32`
7 678×	`lower-*.f64`
7 678×	`lower-*.f32`
3 412×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	440	4779
1	1355	4532
2	3977	4493
0	8628	4244

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

Calls

Call 1

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

rewrite183.0ms (1.1%)

Memory

1.7MiB live, 286.9MiB allocated

Rules

5 312×	`lower-*.f32`
5 284×	`lower-*.f64`
4 604×	`lower-fma.f32`
4 592×	`lower-fma.f64`
3 588×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	331
0	102	325
1	364	325
2	2826	325
0	8708	321

Stop Event

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

Counts

23 → 295

Calls

Call 1

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

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

eval81.0ms (0.5%)

Memory: 22.3MiB live, 220.2MiB allocated
Compiler: Compiled 17 411 to 1 221 computations (93% saved)

prune142.0ms (0.8%)

Memory

-28.5MiB live, 336.5MiB allocated

Pruning

31 alts after pruning (23 fresh and 8 done)

	Pruned	Kept	Total
New	737	12	749
Fresh	5	11	16
Picked	1	4	5
Done	0	4	4
Total	743	31	774

Accuracy

100.0%

Counts

774 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.5%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
✓	54.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	35.2%	(.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 (.f64 (.f64 eps eps) eps) (*.f64 eps 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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
▶	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)))
	85.4%	#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)))
✓	53.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	53.3%	#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)))
✓	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.4%	#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))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))) eps))
✓	99.4%	#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))
✓	80.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
▶	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	54.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.3%	#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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
▶	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
	97.9%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/4 binary64) #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.9%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	79.7%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x) x))))
▶	79.7%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))

Compiler

Compiled 907 to 525 computations (42.1% saved)

simplify207.0ms (1.2%)

Memory

16.7MiB live, 174.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #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(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
cost-diff	0	#s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
cost-diff	0	(neg.f64 eps)
cost-diff	0	(.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) eps)
cost-diff	0	#s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
cost-diff	320	(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
cost-diff	0	(sin.f64 x)
cost-diff	0	(neg.f64 (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)))
cost-diff	320	(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))

Rules

14 046×	`lower-fma.f32`
14 038×	`lower-fma.f64`
4 386×	`lower-*.f32`
4 370×	`lower-*.f64`
1 742×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	449
0	101	440
1	195	437
2	351	429
3	723	419
4	1530	413
5	2529	413
6	4452	413
7	5832	413
8	6589	413
9	6809	413
10	6917	413
11	6997	413
12	7646	413
0	8015	392

Stop Event

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

Calls

Call 1

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

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

localize328.0ms (1.9%)

Memory

-2.5MiB live, 356.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.06652107453094697	(cos.f64 (+.f64 x eps))
accuracy	0.9035845240140984	#s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))
accuracy	1.251458454869278	#s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))
accuracy	29.10413501852235	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
accuracy	0.00390625	(.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
accuracy	0.0078125	(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
accuracy	0.9769345993230975	#s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
accuracy	12.430213897098842	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
accuracy	0	(neg.f64 x)
accuracy	0.11328125	(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))
accuracy	0.3128283084426344	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
accuracy	1.3042332623988235	#s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))
accuracy	0	(neg.f64 x)
accuracy	0.2838621846486539	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
accuracy	1.2767893787002682	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))
accuracy	12.49774534939206	#s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))
accuracy	0.0078125	(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.01171875	(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
accuracy	0.015625	(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))
accuracy	0.3128283084426344	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)))

Samples

220.0ms	176×	2	valid
70.0ms	75×	1	valid
2.0ms	5×	0	valid

Compiler

Compiled 242 to 62 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 235.0ms

ival-mult: 87.0ms (37% of total)

ival-cos: 54.0ms (23% of total)

adjust: 44.0ms (18.7% of total)

ival-add: 25.0ms (10.6% of total)

const: 14.0ms (6% of total)

ival-neg: 4.0ms (1.7% of total)

ival-sub: 3.0ms (1.3% of total)

ival-sin: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series36.0ms (0.2%)

Memory

-16.6MiB live, 20.9MiB allocated

Counts

25 → 492

Calls

Call 1

Inputs
#s(alt (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) (patch (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) #<representation binary64>) () ())
#s(alt (neg.f64 (sin.f64 x)) (patch (neg.f64 (sin.f64 x)) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (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) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (neg.f64 x) eps)) (patch #s(approx (+ ( (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) (patch #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) eps) (patch (.f64 #s(literal -1/2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) #<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(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) (patch #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) (patch (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) (patch (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) (patch (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) (patch (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) (patch (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#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) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (neg.f64 x) eps)) (patch #s(approx (+ ( (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
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#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) (patch #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) (patch #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) (patch #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) (patch #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) (patch (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))) #<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) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) (patch #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) (patch #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) (patch #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) (patch #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) (patch (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) (patch (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) (patch (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) (patch (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 1/120 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (- (cos (+ x eps)) (cos x)) (neg (sin x)) (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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (* (neg x) eps) (+ (* (* -1/2 eps) eps) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (* (* -1/2 (cos x)) eps) eps) (* (* -1/2 (cos x)) eps) (neg x) (+ (* 1/120 (* x x)) -1/6) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1))
3.0ms	eps	@	0	((+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (- (cos (+ x eps)) (cos x)) (neg (sin x)) (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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (* (neg x) eps) (+ (* (* -1/2 eps) eps) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (* (* -1/2 (cos x)) eps) eps) (* (* -1/2 (cos x)) eps) (neg x) (+ (* 1/120 (* x x)) -1/6) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1))
3.0ms	eps	@	inf	((+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (- (cos (+ x eps)) (cos x)) (neg (sin x)) (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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (* (neg x) eps) (+ (* (* -1/2 eps) eps) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (* (* -1/2 (cos x)) eps) eps) (* (* -1/2 (cos x)) eps) (neg x) (+ (* 1/120 (* x x)) -1/6) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1))
3.0ms	x	@	-inf	((+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (- (cos (+ x eps)) (cos x)) (neg (sin x)) (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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (* (neg x) eps) (+ (* (* -1/2 eps) eps) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (* (* -1/2 (cos x)) eps) eps) (* (* -1/2 (cos x)) eps) (neg x) (+ (* 1/120 (* x x)) -1/6) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1))
2.0ms	eps	@	-inf	((+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (- (cos (+ x eps)) (cos x)) (neg (sin x)) (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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (* (neg x) eps) (+ (* (* -1/2 eps) eps) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* (* (* -1/2 (cos x)) eps) eps) (* (* -1/2 (cos x)) eps) (neg x) (+ (* 1/120 (* x x)) -1/6) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1))

simplify150.0ms (0.9%)

Memory

13.3MiB live, 51.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 010×	`lower-fma.f64`
12 010×	`lower-fma.f32`
6 018×	`lower-*.f64`
6 018×	`lower-*.f32`
3 522×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	335	4288
1	1015	4218
2	2961	4125
0	8140	3952

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 484

Calls

Call 1

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

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

rewrite176.0ms (1%)

Memory

-8.3MiB live, 70.2MiB allocated

Rules

8 792×	`lower-fma.f32`
8 784×	`lower-fma.f64`
5 616×	`lower-*.f32`
5 600×	`lower-*.f64`
3 884×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	394
0	101	385
1	400	382
2	2674	382
0	9876	363

Stop Event

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

Counts

25 → 265

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps) eps) (/.f64 (.f64 eps (-.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))) (-.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (neg.f64 (sin.f64 x)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))))))
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(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)
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(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 x eps))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (.f64 (sin.f64 eps) (sin.f64 x))))
(.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(pow.f64 (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)))) (neg.f64 (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 x x) (*.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (fma.f64 eps eps (-.f64 (.f64 x x) (*.f64 eps x))))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
#s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64)))
(.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 (cos.f64 x) eps))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x))
(.f64 (.f64 eps eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(.f64 (cos.f64 x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps))
(.f64 #s(literal -1/2 binary64) (.f64 (*.f64 (cos.f64 x) eps) eps))
(.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) (*.f64 eps eps)))
(.f64 eps (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps))
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))
(.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (neg.f64 x))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) (/.f64 (.f64 (.f64 x x) x) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)) #s(literal 1/36 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)))))
(fma.f64 (*.f64 #s(literal 1/120 binary64) x) x #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 x (*.f64 #s(literal 1/120 binary64) x) #s(literal -1/6 binary64))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))) (/.f64 (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
#s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))

eval73.0ms (0.4%)

Memory: 25.4MiB live, 62.1MiB allocated
Compiler: Compiled 14 341 to 1 090 computations (92.4% saved)

prune144.0ms (0.8%)

Memory

-18.3MiB live, 70.3MiB allocated

Pruning

33 alts after pruning (21 fresh and 12 done)

	Pruned	Kept	Total
New	795	9	804
Fresh	6	12	18
Picked	1	4	5
Done	0	8	8
Total	802	33	835

Accuracy

100.0%

Counts

835 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.5%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
✓	54.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
	35.2%	(.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 (.f64 (.f64 eps eps) eps) (*.f64 eps 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 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) eps) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps)))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) eps) (*.f64 #s(literal -1/2 binary64) eps)) eps)))
	85.4%	#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)))
✓	53.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	53.3%	#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)))
✓	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.4%	#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))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))) eps))
✓	99.4%	#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))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
✓	80.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	54.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.3%	#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 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
✓	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.8%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) x)) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps))))
	79.8%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) (.f64 x x)))))
✓	79.7%	#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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (neg.f64 x) eps))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))

Compiler

Compiled 1 283 to 496 computations (61.3% saved)

regimes35.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

51 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

-23.2MiB 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) (* (+ (* (* 1/6 eps) eps) -1) 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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) 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) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/4 binary64) #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 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 eps (fma.f64 x #s(literal 1/4 binary64) (.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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x) x))))
#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) 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 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 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) eps) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #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 (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))

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:

10.0ms	x
10.0ms	eps
9.0ms	(-.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 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

39 → 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) (* (+ (* (* 1/6 eps) eps) -1) 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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) 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) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/4 binary64) #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 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 eps (fma.f64 x #s(literal 1/4 binary64) (.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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x) x))))
#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) 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 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 (neg.f64 (sin.f64 x)) eps (.f64 #s(approx ( (* -1/2 (cos x)) eps) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #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
9.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory

-25.6MiB live, 14.0MiB allocated

Counts

36 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

35 → 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) (* (+ (* (* 1/6 eps) eps) -1) 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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (neg.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) 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) (fma.f64 #s(approx (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/4 binary64) #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 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 eps (fma.f64 x #s(literal 1/4 binary64) (.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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (neg (sin x)) eps) (* (* (* -1/2 (cos x)) eps) eps)) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (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) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* -1/2 eps) (cos x)) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) eps (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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) (* (+ (* (* 1/6 eps) eps) -1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps) x)) x) x))))
#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) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) 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 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(approx (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

8.0ms	eps
8.0ms	x
7.0ms	(-.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 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-30.4MiB live, 9.2MiB allocated

Counts

19 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`eps`
97.9%	1	`x`
97.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

17 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.9%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* (* eps x) eps) 1/4) (* (+ (* (* 1/6 eps) eps) -1) 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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) 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)) (.f64 #s(approx (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (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
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% 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) (* (+ (* (* 1/6 eps) eps) -1) 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 (+ ( (* -1/2 eps) (cos x)) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))

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
79.7%	1	`x`
79.7%	1	`eps`
79.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (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
53.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
53.1%	1	`x`
53.1%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Rules

52×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	370
1	153	370
2	166	370
3	176	370
4	177	370

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (6.8%)

Memory

-18.5MiB live, 22.3MiB allocated

Rules

14 432×	`lower-fma.f64`
14 432×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
12 448×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	331
0	102	325
1	364	325
2	2826	325
0	8708	321
0	440	4779
1	1355	4532
2	3977	4493
0	8628	4244
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	413	4038
1	1254	3853
2	3494	3791
0	8044	3553
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474
0	335	4288
1	1015	4218
2	2961	4125
0	8140	3952

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 414 to 242 computations (41.5% saved)

preprocess110.0ms (0.6%)

Memory: -8.7MiB live, 68.9MiB allocated
Compiler: Compiled 408 to 174 computations (57.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze74.0ms (0.4%)

sample10.3s (59.7%)

explain291.0ms (1.7%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize105.0ms (0.6%)

series5.0ms (0%)

simplify149.0ms (0.9%)

rewrite188.0ms (1.1%)

eval35.0ms (0.2%)

prune49.0ms (0.3%)

simplify393.0ms (2.3%)

localize401.0ms (2.3%)

series120.0ms (0.7%)

simplify287.0ms (1.7%)

rewrite240.0ms (1.4%)

eval214.0ms (1.2%)

prune330.0ms (1.9%)

simplify150.0ms (0.9%)

localize633.0ms (3.7%)

series46.0ms (0.3%)

simplify162.0ms (0.9%)

rewrite183.0ms (1.1%)

eval81.0ms (0.5%)

prune142.0ms (0.8%)

simplify207.0ms (1.2%)

localize328.0ms (1.9%)

series36.0ms (0.2%)

simplify150.0ms (0.9%)

rewrite176.0ms (1%)

eval73.0ms (0.4%)

prune144.0ms (0.8%)

regimes35.0ms (0.2%)

regimes31.0ms (0.2%)

regimes28.0ms (0.2%)

regimes26.0ms (0.2%)

regimes25.0ms (0.1%)

regimes24.0ms (0.1%)

regimes16.0ms (0.1%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

regimes7.0ms (0%)

regimes6.0ms (0%)

regimes3.0ms (0%)

simplify9.0ms (0%)

soundness1.2s (6.8%)

preprocess110.0ms (0.6%)

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