Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze43.0ms (0.3%)

Memory

8.3MiB live, 46.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.7s (58.6%)

Memory

102.9MiB live, 12 287.0MiB allocated

Samples

3.8s	25 913×	0	invalid
3.6s	5 666×	2	valid
692.0ms	2 470×	1	valid
30.0ms	120×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.2s

ival-cos: 3.1s (49.6% of total)

const: 729.0ms (11.7% of total)

ival-mult: 444.0ms (7.2% of total)

adjust: 394.0ms (6.3% of total)

ival-<=: 334.0ms (5.4% of total)

ival-<: 289.0ms (4.7% of total)

ival-sub: 284.0ms (4.6% of total)

ival-fabs: 277.0ms (4.5% of total)

ival-add: 211.0ms (3.4% of total)

ival-and: 107.0ms (1.7% of total)

exact: 45.0ms (0.7% of total)

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

Bogosity

explain289.0ms (1.8%)

Memory

-17.7MiB live, 350.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
138	3	(8.7290648746166e-161 1.8298224435357222e-163)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	141	0

Confusion

	Predicted +	Predicted -
+	138	1
-	3	114

Precision

0.9787234042553191

Recall

0.9928057553956835

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	1	0
-	3	0	114

Precision?

0.9788732394366197

Recall?

1.0

Freqs

test

number	freq
0	115
1	141

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

150.0ms	340×	2	valid
30.0ms	160×	1	valid
2.0ms	12×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-cos: 95.0ms (64.5% of total)

adjust: 43.0ms (29.2% of total)

ival-sub: 6.0ms (4.1% of total)

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

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

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

preprocess68.0ms (0.4%)

Memory

-10.6MiB live, 28.6MiB 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))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize210.0ms (1.3%)

Memory

-5.0MiB live, 75.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.030522582778191552	(cos.f64 (+.f64 x eps))
accuracy	31.169400006030216	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

191.0ms	170×	2	valid
10.0ms	80×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

adjust: 89.0ms (47.1% of total)

ival-add: 50.0ms (26.5% of total)

ival-cos: 46.0ms (24.4% of total)

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

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

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

series4.0ms (0%)

Memory

5.3MiB live, 5.3MiB 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 (- (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 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 (* -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 (* -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 (+ 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 (- 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 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 (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 (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 (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 (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 (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 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 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 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 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 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 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 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 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 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

21 calls:

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

simplify401.0ms (2.4%)

Memory

16.2MiB live, 283.7MiB 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	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(- (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 x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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 x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

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

rewrite318.0ms (1.9%)

Memory

13.3MiB live, 412.5MiB 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
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(+.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (+.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64)) (cos.f64 x))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 (+.f64 x eps)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
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(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps))) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)) (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))))
(.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (/.f64 (+.f64 x eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))))
(.f64 (.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 x)
(cos.f64 (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))

eval38.0ms (0.2%)

Memory: -1.5MiB live, 74.4MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune53.0ms (0.3%)

Memory

-16.4MiB live, 108.7MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	294	12	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	294	13	307

Accuracy

99.9%

Counts

307 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.3%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
✓	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	50.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	50.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	49.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	50.4%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
▶	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Compiler

Compiled 389 to 256 computations (34.2% saved)

simplify250.0ms (1.5%)

Memory

-15.6MiB live, 399.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

16 964×	`lower-fma.f32`
16 960×	`lower-fma.f64`
3 818×	`lower-*.f32`
3 798×	`lower-*.f64`
3 262×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	247
0	70	237
1	115	237
2	246	237
3	433	229
4	610	229
5	1137	229
6	3126	229
7	4572	229
8	7444	229
0	8136	224

Stop Event

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

Calls

Call 1

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

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

localize272.0ms (1.6%)

Memory

6.6MiB live, 524.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy	0.03125	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy	0.14453125	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
accuracy	0.5348035019920677	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
accuracy	0.0078125	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.030522582778191552	(cos.f64 (+.f64 x eps))
accuracy	0.7576617767861595	#s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
accuracy	31.169400006030216	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy	14.540646554845036	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(cos.f64 eps)
accuracy	30.805384801115704	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	31.720744626176256	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.05329631324130752	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.1328125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.23828125	(+.f64 x (+.f64 x eps))

Samples

163.0ms	175×	2	valid
36.0ms	77×	1	valid
3.0ms	3×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 206 to 38 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 160.0ms

ival-cos: 72.0ms (45.1% of total)

adjust: 30.0ms (18.8% of total)

ival-mult: 28.0ms (17.5% of total)

ival-add: 10.0ms (6.3% of total)

ival-sub: 7.0ms (4.4% of total)

ival-sin: 7.0ms (4.4% of total)

const: 5.0ms (3.1% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series37.0ms (0.2%)

Memory

0.8MiB live, 77.6MiB allocated

Counts

22 → 444

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x 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 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x 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 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #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 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1/2 (* eps (cos x))) (taylor 0 eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf eps) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 eps) (taylor 0 x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) (taylor 0 x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) (taylor 0 x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x (+.f64 x eps)) (patch (+.f64 x (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor 0 x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) (taylor 0 x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) (taylor 0 x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) (taylor 0 x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* 1/2 (* eps (cos x)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor -inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())

Calls

111 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
2.0ms	eps	@	-inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	0	(* (sin x) (neg eps))

simplify238.0ms (1.4%)

Memory

17.0MiB live, 250.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 248×	`lower-fma.f64`
11 248×	`lower-fma.f32`
5 320×	`lower-*.f64`
5 320×	`lower-*.f32`
3 772×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	372	3754
1	1122	3589
2	2974	3546
3	7002	3546
0	8099	3342

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 419

Calls

Call 1

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

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 eps (sin.f64 (neg.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 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)))))))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
(+ (* -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))))))
(fma.f64 x (fma.f64 x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 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))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/48 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* 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))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) (.f64 (sin.f64 eps) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps 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 eps (sin.f64 (neg.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (sin.f64 (neg.f64 x))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
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(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)))))
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* -1 (sin x))
(sin.f64 (neg.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64))) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))

rewrite248.0ms (1.5%)

Memory

-24.4MiB live, 182.4MiB allocated

Rules

4 544×	`lower-fma.f32`
4 542×	`lower-*.f32`
4 540×	`lower-fma.f64`
4 522×	`lower-*.f64`
4 282×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	188
0	70	182
1	239	182
2	1825	182
0	8795	177

Stop Event

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

Counts

22 → 578

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 x (+.f64 x eps))))) (neg.f64 (neg.f64 (-.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(/.f64 (fma.f64 eps (.f64 eps eps) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 #s(literal 2 binary64) x eps) (-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 0 binary64)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (-.f64 (.f64 eps eps) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) eps))))
(pow.f64 (/.f64 (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 x (+.f64 x eps)))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (*.f64 x x))))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 x (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 x eps))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal -1/2 binary64)))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 x #s(literal -1/2 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) x (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64)))) (-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) x)) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)

eval111.0ms (0.7%)

Memory: 13.2MiB live, 93.0MiB allocated
Compiler: Compiled 25 423 to 2 934 computations (88.5% saved)

prune132.0ms (0.8%)

Memory

-7.4MiB live, 109.5MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	1 054	20	1 074
Fresh	6	1	7
Picked	2	3	5
Done	0	1	1
Total	1 062	25	1 087

Accuracy

100.0%

Counts

1 087 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.3%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
✓	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	50.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
▶	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
▶	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
	76.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))

Compiler

Compiled 824 to 486 computations (41% saved)

simplify191.0ms (1.2%)

Memory

2.6MiB live, 84.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
cost-diff	0	#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
cost-diff	128	(fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
cost-diff	320	(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
cost-diff	0	(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
cost-diff	0	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))
cost-diff	0	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 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	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

16 872×	`lower-fma.f32`
16 858×	`lower-fma.f64`
5 476×	`lower-*.f32`
5 448×	`lower-*.f64`
1 664×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	483
0	108	488
1	197	460
2	492	423
3	1119	420
4	2929	417
5	5690	417
0	8042	413

Stop Event

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

Calls

Call 1

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

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

localize342.0ms (2.1%)

Memory

-10.7MiB live, 110.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.01953125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
accuracy	0.05329631324130752	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.1328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.25	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
accuracy	0.375	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.5348035019920677	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
accuracy	1.0430278879884562	#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
accuracy	0.0078125	(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
accuracy	0.14453125	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))))
accuracy	0.5348035019920677	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
accuracy	1.7097811210655829	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))
accuracy	0.5748259508697983	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	30.805384801115704	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	31.720744626176256	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0.015625	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
accuracy	0.0234375	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.1328125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

201.0ms	174×	2	valid
54.0ms	77×	1	valid
3.0ms	1×	3	valid
3.0ms	3×	0	valid
2.0ms	1×	5	exit

Compiler

Compiled 371 to 65 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 216.0ms

ival-cos: 71.0ms (32.9% of total)

adjust: 48.0ms (22.2% of total)

ival-mult: 48.0ms (22.2% of total)

ival-add: 19.0ms (8.8% of total)

ival-sin: 14.0ms (6.5% of total)

const: 7.0ms (3.2% of total)

ival-sub: 5.0ms (2.3% of total)

ival-neg: 2.0ms (0.9% of total)

exact: 1.0ms (0.5% of total)

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

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

series40.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

24 → 504

Calls

Call 1

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

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

Calls

126 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps)))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	eps	@	inf	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps)))
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

simplify234.0ms (1.4%)

Memory

1.0MiB live, 108.4MiB allocated

Algorithm

1×	egg-herbie

Rules

13 114×	`lower-fma.f64`
13 114×	`lower-fma.f32`
7 510×	`lower-*.f64`
7 510×	`lower-*.f32`
3 116×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	438	6006
1	1346	5776
2	3872	5744
0	8221	5378

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 480

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
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)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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 (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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))
(* -1/2 (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))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
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)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos 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 x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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 (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 (* (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 (* (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 (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)))))))
(* 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)))
(* 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 (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)))
(* 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 (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 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)))
(- (* -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))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* -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)))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* -1 eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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 (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 (* (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 (* (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 (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)))))))
(* 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)))
(* 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 (* 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)))))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* 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 (* 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 (- (* 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)))))
(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 (* 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 (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 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 (* 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 (* 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))))
(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 (+ 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 (* 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))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(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 x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 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))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(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))))))))
(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)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(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)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 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)))

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

rewrite146.0ms (0.9%)

Memory

-3.1MiB live, 50.8MiB allocated

Rules

2 748×	`lower-fma.f32`
2 734×	`lower-fma.f64`
1 870×	`lower-*.f32`
1 844×	`lower-*.f64`
1 058×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	390
0	108	362
1	393	306
0	3444	306

Stop Event

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

Counts

24 → 310

Calls

Call 1

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

Outputs
#s(literal 0 binary64)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (neg.f64 eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (neg.f64 eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (+.f64 x eps) eps))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x))
(fma.f64 (*.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) (.f64 (fma.f64 x x (*.f64 (+.f64 x eps) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 x x (*.f64 (+.f64 x eps) eps)))
(/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 eps (neg.f64 eps)) (neg.f64 eps))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 eps eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps)) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x eps) eps))))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 x (+.f64 x eps)))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps)
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (+.f64 x eps) eps))))
(.f64 (.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(literal 0 binary64))))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(literal 0 binary64)))) #s(literal -2 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (neg.f64 (cos.f64 x))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
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(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (fma.f64 eps #s(literal 1/4 binary64) (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (neg.f64 (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (neg.f64 (fma.f64 eps #s(literal 1/4 binary64) (*.f64 #s(literal -1/6 binary64) x))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64)))))
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(literal 1/4 binary64) (.f64 #s(literal -1/6 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))

eval79.0ms (0.5%)

Memory: -7.7MiB live, 66.7MiB allocated
Compiler: Compiled 18 296 to 1 470 computations (92% saved)

prune116.0ms (0.7%)

Memory

-5.4MiB live, 81.2MiB allocated

Pruning

32 alts after pruning (25 fresh and 7 done)

	Pruned	Kept	Total
New	774	17	791
Fresh	8	8	16
Picked	2	3	5
Done	0	4	4
Total	784	32	816

Accuracy

100.0%

Counts

816 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.3%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
✓	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	50.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
▶	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
▶	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
✓	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	76.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
▶	76.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
	96.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))

Compiler

Compiled 1 028 to 588 computations (42.8% saved)

simplify263.0ms (1.6%)

Memory

3.0MiB live, 113.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
cost-diff	0	(fma.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)
cost-diff	0	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x))
cost-diff	0	(.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
cost-diff	0	(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
cost-diff	0	#s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x))
cost-diff	0	(.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
cost-diff	0	#s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))
cost-diff	0	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))
cost-diff	0	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (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))))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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)))))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))

Rules

26 066×	`lower-fma.f32`
26 054×	`lower-fma.f64`
5 182×	`lower-*.f32`
5 152×	`lower-*.f64`
2 842×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	571
0	117	568
1	222	556
2	483	527
3	814	527
4	1848	527
5	3687	527
6	5988	527
0	8081	515

Stop Event

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

Calls

Call 1

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

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

localize350.0ms (2.1%)

Memory

-7.1MiB live, 117.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05329631324130752	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.1328125	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.26430543072389573	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.31640625	(*.f64 eps #s(literal -1/48 binary64))
accuracy	0.05859375	(*.f64 x #s(literal 1/120 binary64))
accuracy	0.3515625	(.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
accuracy	0.7122581427354175	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x))
accuracy	14.540646554845036	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
accuracy	0.00390625	(.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps))
accuracy	0.171875	(.f64 #s(literal -1/6 binary64) (.f64 x x))
accuracy	1.0864348885965371	#s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x))
accuracy	14.540646554845036	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
accuracy	0.14453125	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))))
accuracy	0.5348035019920677	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
accuracy	1.7097811210655829	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))
accuracy	25.901693062421376	#s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))
accuracy	0.015625	(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01953125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))
accuracy	0.0234375	(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)))))
accuracy	0.1328125	(.f64 (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))))))

Samples

212.0ms	165×	2	valid
62.0ms	82×	1	valid
4.0ms	2×	5	exit
3.0ms	6×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 343 to 71 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 216.0ms

ival-mult: 63.0ms (29.2% of total)

adjust: 49.0ms (22.7% of total)

ival-cos: 49.0ms (22.7% of total)

ival-add: 18.0ms (8.3% of total)

ival-sin: 14.0ms (6.5% of total)

const: 12.0ms (5.6% of total)

ival-sub: 5.0ms (2.3% of total)

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

exact: 1.0ms (0.5% of total)

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

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

series27.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

27 → 528

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) (patch #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #<representation binary64>) () ())
#s(alt (.f64 (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)))))) (patch (.f64 (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)))))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))) (patch (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) (patch #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)) (patch #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) (neg.f64 eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) (neg.f64 eps)) (patch (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x) (patch (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)) (patch (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (patch #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) (patch (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (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))))) (patch (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))))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/6 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/6 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/120 binary64)) (patch (.f64 x #s(literal 1/120 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())

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

Calls

132 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* x x) (* (+ (* x (* x 1/120)) -1/6) x)) x)
0.0ms	x	@	-inf	(+ (* (* x x) (* (+ (* x (* x 1/120)) -1/6) x)) x)
0.0ms	x	@	inf	(+ (* x (* -1/6 (* x x))) x)
0.0ms	x	@	-inf	(* x 1/120)
0.0ms	eps	@	inf	(* eps -1/48)

simplify235.0ms (1.4%)

Memory

-14.3MiB live, 101.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 320×	`lower-fma.f64`
12 320×	`lower-fma.f32`
5 798×	`lower-*.f64`
5 798×	`lower-*.f32`
4 110×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	6062
1	1185	5832
2	3281	5737
3	7581	5737
0	8079	5405

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 524

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)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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 (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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 (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 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 x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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 (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 (* (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 (* (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 (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)))))))
(* 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)))
(* 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 (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)))
(* 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 (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 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)))
(- (* -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))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 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 x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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 x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -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))
(* -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)))))
(- (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 x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps 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)))
(* 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 (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (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 x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
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) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -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)))))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* -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))))))
(* 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 (* 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 (- (* 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)))))
(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 (* 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 (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 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 (* 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 (* 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))))
(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 (+ 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 (* 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))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(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 x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 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))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 x)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 3))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(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))))))))
(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)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(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)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 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)))

Outputs
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* 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 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (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)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (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)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (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)))))))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(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)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(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)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(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)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(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)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(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)))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(fma.f64 (.f64 x x) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(.f64 (.f64 eps (cos.f64 x)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(.f64 eps (fma.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(.f64 eps (fma.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* 1/120 (pow x 3))
(.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* 1/120 (pow x 3))
(.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite194.0ms (1.2%)

Memory

22.2MiB live, 93.0MiB allocated

Rules

4 164×	`lower-fma.f32`
4 152×	`lower-fma.f64`
3 502×	`lower-/.f64`
3 502×	`lower-/.f32`
3 408×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	506
0	117	458
1	435	404
2	3436	392
0	8622	380

Stop Event

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

Counts

27 → 296

Calls

Call 1

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

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

eval110.0ms (0.7%)

Memory: -19.7MiB live, 72.5MiB allocated
Compiler: Compiled 21 293 to 1 455 computations (93.2% saved)

prune145.0ms (0.9%)

Memory

4.3MiB live, 83.0MiB allocated

Pruning

31 alts after pruning (20 fresh and 11 done)

	Pruned	Kept	Total
New	866	5	871
Fresh	5	15	20
Picked	1	4	5
Done	0	7	7
Total	872	31	903

Accuracy

100.0%

Counts

903 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	50.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	49.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	77.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
✓	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
✓	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
✓	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	76.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
✓	76.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
	77.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	50.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	76.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
	96.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))

Compiler

Compiled 1 483 to 562 computations (62.1% saved)

regimes38.0ms (0.2%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

55 → 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

13.0ms	x
13.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.2%)

Memory

-26.1MiB live, 19.3MiB allocated

Counts

53 → 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))

Outputs

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

Calls

3 calls:

12.0ms	x
12.0ms	eps
12.0ms	(-.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)

regimes33.0ms (0.2%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

47 → 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

-22.7MiB live, 16.4MiB 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Outputs

(*.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)) x) x)) (.f64 #s(literal -1/2 binary64) (*.f64 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))

Outputs

(*.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #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	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.1%)

Memory

-25.9MiB live, 13.4MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs

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

regimes22.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

30 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	x
7.0ms	eps
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-29.3MiB live, 10.2MiB 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps))) (.f64 (.f64 x eps) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`eps`
97.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.3%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.2%	1	`x`
97.2%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

3 → 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
76.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
76.6%	1	`x`
76.6%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.1%	1	`eps`
49.1%	1	`x`
49.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

-36.5MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Rules

78×	`*-commutative_binary64`
18×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	491
1	200	491
2	216	491
3	227	491
4	232	491

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#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 (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (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))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (neg.f64 eps) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#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)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))

soundness1.2s (7.2%)

Memory

26.8MiB live, 26.8MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 114×	`lower-fma.f64`
13 114×	`lower-fma.f32`
11 248×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	372	3754
1	1122	3589
2	2974	3546
3	7002	3546
0	8099	3342
0	438	6006
1	1346	5776
2	3872	5744
0	8221	5378
0	42	188
0	70	182
1	239	182
2	1825	182
0	8795	177
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Compiler

Compiled 555 to 307 computations (44.7% saved)

preprocess141.0ms (0.9%)

Memory: 6.3MiB live, 84.4MiB allocated
Compiler: Compiled 556 to 218 computations (60.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze43.0ms (0.3%)

sample9.7s (58.6%)

explain289.0ms (1.8%)

preprocess68.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize210.0ms (1.3%)

series4.0ms (0%)

simplify401.0ms (2.4%)

rewrite318.0ms (1.9%)

eval38.0ms (0.2%)

prune53.0ms (0.3%)

simplify250.0ms (1.5%)

localize272.0ms (1.6%)

series37.0ms (0.2%)

simplify238.0ms (1.4%)

rewrite248.0ms (1.5%)

eval111.0ms (0.7%)

prune132.0ms (0.8%)

simplify191.0ms (1.2%)

localize342.0ms (2.1%)

series40.0ms (0.2%)

simplify234.0ms (1.4%)

rewrite146.0ms (0.9%)

eval79.0ms (0.5%)

prune116.0ms (0.7%)

simplify263.0ms (1.6%)

localize350.0ms (2.1%)

series27.0ms (0.2%)

simplify235.0ms (1.4%)

rewrite194.0ms (1.2%)

eval110.0ms (0.7%)

prune145.0ms (0.9%)

regimes38.0ms (0.2%)

regimes39.0ms (0.2%)

regimes33.0ms (0.2%)

regimes31.0ms (0.2%)

regimes27.0ms (0.2%)

regimes26.0ms (0.2%)

regimes24.0ms (0.1%)

regimes22.0ms (0.1%)

regimes21.0ms (0.1%)

regimes17.0ms (0.1%)

regimes13.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify12.0ms (0.1%)

soundness1.2s (7.2%)

preprocess141.0ms (0.9%)

end0.0ms (0%)

Profiling

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

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