Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze44.0ms (0.4%)

Memory

37.8MiB live, 74.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.2s (57.8%)

Memory

-170.6MiB live, 7 066.9MiB allocated

Samples

4.0s	26 485×	0	invalid
653.0ms	5 506×	0	valid
571.0ms	2 750×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.8s

const: 1.1s (29% of total)

ival-sin: 735.0ms (19.3% of total)

ival-<=: 370.0ms (9.7% of total)

ival-mult: 342.0ms (9% of total)

ival-fabs: 272.0ms (7.1% of total)

ival-<: 244.0ms (6.4% of total)

ival-add: 238.0ms (6.3% of total)

ival-sub: 223.0ms (5.9% of total)

ival-and: 111.0ms (2.9% of total)

adjust: 103.0ms (2.7% of total)

exact: 51.0ms (1.3% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain87.0ms (0.7%)

Memory

3.8MiB live, 118.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
219	3	(6.242247982204401e-307 9.6704971108971e-310)	5	(2.2515483542545645e-130 4.1163029816477274e-132)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	217	11

Confusion

	Predicted +	Predicted -
+	214	5
-	3	34

Precision

0.9861751152073732

Recall

0.9771689497716894

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	214	5	0
-	3	6	28

Precision?

0.9605263157894737

Recall?

1.0

Freqs

test

number	freq
0	39
1	217

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

20.0ms	176×	1	valid
17.0ms	334×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sin: 10.0ms (47% of total)

adjust: 4.0ms (18.8% of total)

ival-add: 3.0ms (14.1% of total)

ival-sub: 3.0ms (14.1% of total)

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

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

preprocess22.0ms (0.2%)

Memory

22.1MiB live, 22.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (0.3%)

Memory

-11.6MiB live, 28.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.01171875	(sin.f64 (+.f64 x eps))
accuracy	23.59903355009003	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

17.0ms	167×	0	valid
9.0ms	88×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-add: 9.0ms (51.1% of total)

ival-sin: 5.0ms (28.4% of total)

adjust: 2.0ms (11.4% of total)

ival-sub: 2.0ms (11.4% of total)

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

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

series5.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.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 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify149.0ms (1.2%)

Memory

-9.1MiB live, 153.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite179.0ms (1.4%)

Memory

21.6MiB live, 132.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

Outputs
#<batchref>
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eval52.0ms (0.4%)

Memory: -13.8MiB live, 65.7MiB allocated
Compiler: Compiled 6 625 to 852 computations (87.1% saved)

prune9.0ms (0.1%)

Memory

-12.5MiB live, 26.1MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	285	6	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	285	7	292

Accuracy

100.0%

Counts

292 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	100.0%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 133 to 110 computations (17.3% saved)

simplify201.0ms (1.6%)

Memory

23.6MiB live, 139.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sin.f64 eps) x)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	203
0	60	193
1	99	193
2	182	193
3	359	193
4	633	193
5	945	193
6	1317	193
7	2189	193
8	2751	193
9	2998	190
10	3229	190
11	3570	190
12	5142	190
13	6380	190
0	8468	188

Stop Event

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

Calls

Call 1

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

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

localize251.0ms (2%)

Memory

-16.2MiB live, 290.7MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
accuracy	0.15360128162065376	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.5486323406702114	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
accuracy	28.973599239681477	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.01171875	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(*.f64 (cos.f64 x) eps)
accuracy	0.5250219437797615	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0	(sin.f64 eps)
accuracy	1.0127701367688962	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Samples

194.0ms	252×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 355 to 69 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-cos: 64.0ms (39.3% of total)

adjust: 38.0ms (23.4% of total)

ival-mult: 29.0ms (17.8% of total)

ival-sin: 12.0ms (7.4% of total)

ival-add: 10.0ms (6.1% of total)

ival-sub: 5.0ms (3.1% of total)

ival-div: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series75.0ms (0.6%)

Memory

-0.7MiB live, 37.2MiB allocated

Counts

20 → 396

Calls

Call 1

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

Outputs
#s(alt (* -1 x) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (cos (* -1 x)) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1))
5.0ms	x	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1))
4.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1))
4.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1))
4.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1))

simplify165.0ms (1.3%)

Memory

-1.5MiB live, 147.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	3712
1	1248	3510
2	3433	3428
0	8199	3203

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 380

Calls

Call 1

Inputs
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
eps
eps
eps
eps
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(* eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
eps
eps
eps
eps
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (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)
(- (cos eps) 1)
(- (cos eps) 1)
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
eps
eps
eps
eps
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (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)
(- (cos eps) 1)
(- (cos eps) 1)
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
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)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* -1/2 (* x (sin eps)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1/2 (* x (sin eps)))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))

Outputs
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
eps
eps
eps
eps
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/6 binary64)) eps) eps (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
(* -1/2 (* eps x))
(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(.f64 (.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps x)
(*.f64 eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(*.f64 x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(.f64 (fma.f64 (.f64 x (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps eps) x) eps)
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) eps) eps (.f64 #s(literal -1/6 binary64) x)) (*.f64 eps x))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
eps
eps
eps
eps
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
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(- (sin (+ eps x)) (sin x))
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(* x (sin eps))
(*.f64 (sin.f64 eps) x)

rewrite151.0ms (1.2%)

Memory

15.1MiB live, 136.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	170
0	60	162
1	210	162
2	1636	162
0	8539	162

Stop Event

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

Counts

20 → 384

Calls

Call 1

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

Outputs
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eval136.0ms (1.1%)

Memory: -20.3MiB live, 133.3MiB allocated
Compiler: Compiled 16 783 to 2 120 computations (87.4% saved)

prune24.0ms (0.2%)

Memory

20.8MiB live, 59.4MiB allocated

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	804	11	815
Fresh	0	1	1
Picked	3	2	5
Done	0	1	1
Total	807	15	822

Accuracy

100.0%

Counts

822 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
▶	100.0%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))

Compiler

Compiled 357 to 281 computations (21.3% saved)

simplify150.0ms (1.2%)

Memory

19.5MiB live, 89.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff	0	(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
cost-diff	0	(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
cost-diff	128	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	373
0	83	371
1	148	371
2	351	371
3	819	371
4	1371	371
5	2023	371
6	2258	371
7	3418	371
8	4846	369
9	6143	369
10	7733	369
0	8029	360

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.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)) #s(literal -2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
eps
#s(literal -1/2 binary64)
(neg.f64 x)
x
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 eps x)
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 x #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 x #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 x #s(literal -1/2 binary64))) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (sin x) -1/2) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
eps
(cos.f64 x)

localize215.0ms (1.7%)

Memory

-29.6MiB live, 259.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
accuracy	0.01171875	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
accuracy	1.0007888720545561	#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
accuracy	0.00390625	(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.0078125	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.4090954945533496	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.5250219437797615	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.13671875	(*.f64 eps (+.f64 eps x))
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
accuracy	0.5172722995162955	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
accuracy	0.01171875	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	1.0674307411265922	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
accuracy	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))

Samples

109.0ms	169×	0	valid
51.0ms	87×	1	valid

Compiler

Compiled 495 to 88 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-mult: 33.0ms (38.2% of total)

ival-add: 16.0ms (18.5% of total)

adjust: 8.0ms (9.3% of total)

ival-sin: 8.0ms (9.3% of total)

const: 8.0ms (9.3% of total)

ival-cos: 6.0ms (6.9% of total)

ival-div: 2.0ms (2.3% of total)

ival-sub: 2.0ms (2.3% of total)

exact: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

series46.0ms (0.4%)

Memory

14.5MiB live, 97.9MiB allocated

Counts

22 → 456

Calls

Call 1

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

Outputs
#s(alt (cos (neg x)) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (sin (* 1/2 eps)) 2) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24))
7.0ms	eps	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (sin (* 1/2 eps)) 2) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24))
6.0ms	x	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (sin (* 1/2 eps)) 2) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24))
4.0ms	eps	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (sin (* 1/2 eps)) 2) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24))
3.0ms	eps	@	0	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (sin (* 1/2 eps)) 2) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24))

simplify179.0ms (1.4%)

Memory

-4.7MiB live, 183.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	379	4536
1	1191	4385
2	2934	4275
3	7112	4275
0	8306	3961

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 450

Calls

Call 1

Inputs
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(* -1 x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 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)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))

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

rewrite251.0ms (2%)

Memory

-0.5MiB live, 197.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	323
0	83	321
1	311	321
2	2537	321
0	8376	315

Stop Event

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

Counts

22 → 527

Calls

Call 1

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

Outputs
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eval173.0ms (1.4%)

Memory: 8.0MiB live, 170.9MiB allocated
Compiler: Compiled 21 769 to 3 055 computations (86% saved)

prune74.0ms (0.6%)

Memory

-19.5MiB live, 65.8MiB allocated

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	986	5	991
Fresh	0	7	7
Picked	2	3	5
Done	0	3	3
Total	988	18	1 006

Accuracy

100.0%

Counts

1 006 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
▶	48.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
▶	100.0%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))

Compiler

Compiled 467 to 343 computations (26.6% saved)

simplify141.0ms (1.1%)

Memory

-0.6MiB live, 75.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	320	(.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))
cost-diff	320	(*.f64 (-.f64 x eps) #s(literal 1 binary64))
cost-diff	576	(/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))
cost-diff	1536	(fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
cost-diff	128	(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))
cost-diff	0	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
cost-diff	0	(fma.f64 eps #s(literal 1/2 binary64) x)
cost-diff	0	(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	663
0	114	651
1	221	651
2	712	587
3	3823	579
0	8251	558

Stop Event

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

Calls

Call 1

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

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

localize266.0ms (2.1%)

Memory

20.1MiB live, 176.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
accuracy	0.5172722995162955	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))
accuracy	0.6311400728373626	(.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))
accuracy	29.962020415373352	(/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))
accuracy	0.014003759768442016	(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps)))
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
accuracy	0.41796875	(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps)
accuracy	0.5172722995162955	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)))
accuracy	0.00390625	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
accuracy	0.006191259768442017	(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)
accuracy	0.4074816774545286	#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))
accuracy	0.5250219437797615	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.3828194155788591	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
accuracy	0.5172722995162955	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps))
accuracy	13.72616068649512	#s(approx (* eps (+ eps x)) (*.f64 eps x))
accuracy	0	(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))

Samples

100.0ms	166×	0	valid
72.0ms	88×	1	valid
1.0ms	1×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 901 to 120 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-mult: 46.0ms (32.3% of total)

ival-neg: 30.0ms (21% of total)

adjust: 20.0ms (14% of total)

ival-add: 15.0ms (10.5% of total)

ival-div: 8.0ms (5.6% of total)

ival-sin: 8.0ms (5.6% of total)

ival-cos: 6.0ms (4.2% of total)

const: 4.0ms (2.8% of total)

ival-sub: 3.0ms (2.1% of total)

exact: 1.0ms (0.7% of total)

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

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

series90.0ms (0.7%)

Memory

7.7MiB live, 44.7MiB allocated

Counts

26 → 588

Calls

Call 1

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

Outputs
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))))))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (/ (+ (* (* x x) 1/2) -1) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (/ (neg eps) (neg (* eps eps))) (* (- x eps) 1) (* (- x eps) (/ (neg eps) (neg (* eps eps)))) (* (sin (* eps 1/2)) 2) (* eps (+ eps x)) (* (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) eps) (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)))
6.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (/ (+ (* (* x x) 1/2) -1) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (/ (neg eps) (neg (* eps eps))) (* (- x eps) 1) (* (- x eps) (/ (neg eps) (neg (* eps eps)))) (* (sin (* eps 1/2)) 2) (* eps (+ eps x)) (* (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) eps) (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)))
6.0ms	eps	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (/ (+ (* (* x x) 1/2) -1) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (/ (neg eps) (neg (* eps eps))) (* (- x eps) 1) (* (- x eps) (/ (neg eps) (neg (* eps eps)))) (* (sin (* eps 1/2)) 2) (* eps (+ eps x)) (* (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) eps) (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)))
5.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (/ (+ (* (* x x) 1/2) -1) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (/ (neg eps) (neg (* eps eps))) (* (- x eps) 1) (* (- x eps) (/ (neg eps) (neg (* eps eps)))) (* (sin (* eps 1/2)) 2) (* eps (+ eps x)) (* (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) eps) (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)))
4.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (/ (+ (* (* x x) 1/2) -1) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (/ (neg eps) (neg (* eps eps))) (* (- x eps) 1) (* (- x eps) (/ (neg eps) (neg (* eps eps)))) (* (sin (* eps 1/2)) 2) (* eps (+ eps x)) (* (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) eps) (+ (* -1/2 x) (/ (+ (* (* x x) 1/2) -1) (neg eps))) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)))

simplify223.0ms (1.8%)

Memory

-5.6MiB live, 110.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	513	6211
1	1598	5837
2	4737	5702
0	8849	5290

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 574

Calls

Call 1

Inputs
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(+ x (* -1/2 (pow x 3)))
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (* -1/2 (* x (+ x (* -1 x)))) 1))))
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1))))
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1))))
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
x
(+ x (* -1 eps))
(+ x (* -1 eps))
(+ x (* -1 eps))
(/ x eps)
(/ (+ x (* -1 eps)) eps)
(/ (+ x (* -1 eps)) eps)
(/ (+ x (* -1 eps)) eps)
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(* -1 (- (* 1/2 (pow x 2)) 1))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 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)
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(* eps (+ 1/2 (/ x eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
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(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
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(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
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(* (pow eps 2) (- (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (+ (* -1/2 (/ (pow x 3) (pow eps 2))) (+ (* 1/2 x) (/ x (pow eps 2))))) (/ 1 eps)))
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(* -1 eps)
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(* eps (- (/ x eps) 1))
(* eps (- (/ x eps) 1))
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(- (/ x eps) 1)
(- (/ x eps) 1)
(- (/ x eps) 1)
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* eps (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* eps (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1/2 x)
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 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 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* 1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/2 (* x (+ x (* -1 x))))) eps)) (* 1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) eps)) (* -1/2 (* x (+ x (* -1 x)))))) eps)) (* 1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) eps)) (* -1/2 (* x (+ x (* -1 x)))))) eps)) (* 1/2 x)))
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
-1
(- (/ x eps) 1)
(- (/ x eps) 1)
(- (/ x eps) 1)
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* -1/2 (* eps x))
(* -1 (* eps (- (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) (/ 1 eps))))
(* -1 (* eps (- (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) (/ 1 eps))))
(* -1 (* eps (- (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) (/ 1 eps))))
(* -1/2 x)
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
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(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(/ 1 eps)
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1 eps)
(- (* x (+ 1 (* 1/2 (pow eps 2)))) eps)
(- (* x (+ 1 (+ (* -1/2 (* x (+ eps (* -1 eps)))) (* 1/2 (pow eps 2))))) eps)
(- (* x (+ 1 (+ (* 1/2 (pow eps 2)) (* x (+ (* -1/2 x) (* -1/2 (+ eps (* -1 eps)))))))) eps)
(* -1 eps)
(- x eps)
(- x eps)
(- x eps)
-1
(- (/ x eps) 1)
(- (/ x eps) 1)
(- (/ x eps) 1)
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(/ 1 eps)
(+ (* -1/2 x) (/ 1 eps))
(+ (* x (- (* -1/2 (/ x eps)) 1/2)) (/ 1 eps))
(+ (* x (- (* -1/2 (/ x eps)) 1/2)) (/ 1 eps))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* -1/2 (/ (pow x 2) eps))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* -1/2 (/ (+ eps (* -1 eps)) x)) 1/2))
(* (pow x 3) (- (+ (* -1/2 (/ (+ eps (* -1 eps)) x)) (+ (* 1/2 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2)))) 1/2))
(* (pow x 3) (- (+ (* -1 (/ eps (pow x 3))) (+ (* -1/2 (/ (+ eps (* -1 eps)) x)) (+ (* 1/2 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2))))) 1/2))
x
(* x (+ 1 (* -1 (/ eps x))))
(* x (+ 1 (* -1 (/ eps x))))
(* x (+ 1 (* -1 (/ eps x))))
(/ x eps)
(* x (- (/ 1 eps) (/ 1 x)))
(* x (- (/ 1 eps) (/ 1 x)))
(* x (- (/ 1 eps) (/ 1 x)))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (/ (pow x 2) eps))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* -1/2 (/ (pow x 2) eps))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (+ 1/2 (* 1/2 (/ (+ eps (* -1 eps)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (pow eps 2)) 1) x)) (* -1/2 (+ eps (* -1 eps)))) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (pow eps 2)) (/ eps x)) 1) x)) (* -1/2 (+ eps (* -1 eps)))) x)))))
x
(* -1 (* x (- (/ eps x) 1)))
(* -1 (* x (- (/ eps x) 1)))
(* -1 (* x (- (/ eps x) 1)))
(/ x eps)
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1/2 (/ (pow x 2) eps))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 (* eps x))) x)) (* 1/2 (/ 1 eps))))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 (* eps x))) x)) (* 1/2 (/ 1 eps))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))

Outputs
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 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)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ x (* -1/2 (pow x 3)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x)
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (* -1/2 (* x (+ x (* -1 x)))) 1))))
(-.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x) eps)
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) eps #s(literal -1 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x))
(+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) eps #s(literal -1 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x))
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
x
(+ x (* -1 eps))
(-.f64 x eps)
(+ x (* -1 eps))
(-.f64 x eps)
(+ x (* -1 eps))
(-.f64 x eps)
(/ x eps)
(/.f64 x eps)
(/ (+ x (* -1 eps)) eps)
(/.f64 (-.f64 x eps) eps)
(/ (+ x (* -1 eps)) eps)
(/.f64 (-.f64 x eps) eps)
(/ (+ x (* -1 eps)) eps)
(/.f64 (-.f64 x eps) eps)
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps x)
(*.f64 x eps)
(* eps (+ eps x))
(*.f64 (+.f64 x eps) eps)
(* eps (+ eps x))
(*.f64 (+.f64 x eps) eps)
(* eps (+ eps x))
(*.f64 (+.f64 x eps) eps)
(* -1 (- (* 1/2 (pow x 2)) 1))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x)))
(fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (/ (- (* 1/2 (pow x 2)) 1) eps))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(/.f64 (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(/.f64 (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(/ (+ (* -1 (- (* 1/2 (pow x 2)) 1)) (* -1/2 (* eps x))) eps)
(/.f64 (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 x x))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x eps) x)) (/.f64 #s(literal 1/2 binary64) eps)) (/.f64 #s(literal 1/2 binary64) x)) (.f64 x x))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x eps) x)) (/.f64 #s(literal 1/2 binary64) eps)) (/.f64 #s(literal 1/2 binary64) x)) (.f64 x x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* 1/24 (* eps (pow x 4)))
(.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(* 1/24 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal 1/24 binary64))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps)) x) x)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps)) x) x)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps)) x) x)
(* -1/2 (/ (pow x 2) eps))
(.f64 (.f64 x (/.f64 x eps)) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x eps) x)) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 x x))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x eps) x)) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 x x))
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x eps) x)) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 x x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* -1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* -1 (* (pow x 3) (+ 1/2 (* 1/2 (/ (+ eps (* -1 eps)) x)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (pow eps 2)) 1) x)) (* -1/2 (+ eps (* -1 eps)))) x)))))
(.f64 (+.f64 (/.f64 (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (pow eps 2)) (/ eps x)) 1) x)) (* -1/2 (+ eps (* -1 eps)))) x)))))
(.f64 (+.f64 (/.f64 (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 eps x))) x) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
x
(* -1 (* x (- (/ eps x) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) x x)
(* -1 (* x (- (/ eps x) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) x x)
(* -1 (* x (- (/ eps x) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) x x)
(/ x eps)
(/.f64 x eps)
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(/.f64 (-.f64 x eps) eps)
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(/.f64 (-.f64 x eps) eps)
(* -1 (* x (- (/ 1 x) (/ 1 eps))))
(/.f64 (-.f64 x eps) eps)
(* eps x)
(*.f64 x eps)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(.f64 (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(* -1/2 (/ (pow x 2) eps))
(.f64 (.f64 x (/.f64 x eps)) #s(literal -1/2 binary64))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 x x))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 (* eps x))) x)) (* 1/2 (/ 1 eps))))
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(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 (* eps x))) x)) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) eps)) x)) (.f64 x x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

rewrite305.0ms (2.5%)

Memory

11.8MiB live, 205.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	516
0	114	478
1	427	469
2	3849	469
0	10710	456

Stop Event

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

Counts

26 → 484

Calls

Call 1

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

Outputs
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eval162.0ms (1.3%)

Memory: 3.9MiB live, 316.2MiB allocated
Compiler: Compiled 27 953 to 3 354 computations (88% saved)

prune64.0ms (0.5%)

Memory

-9.8MiB live, 88.5MiB allocated

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	1 108	4	1 112
Fresh	1	6	7
Picked	3	2	5
Done	0	6	6
Total	1 112	18	1 130

Accuracy

100.0%

Counts

1 130 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	7.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
	51.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
✓	100.0%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))

Compiler

Compiled 638 to 358 computations (43.9% saved)

regimes25.0ms (0.2%)

Memory

5.3MiB live, 43.4MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.2%)

Memory

-18.4MiB live, 56.7MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

14.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

-1.0MiB live, 38.3MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

13.5MiB live, 52.7MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

15.9MiB live, 55.4MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

-16.1MiB live, 30.6MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(approx ( eps (+ eps x)) (*.f64 x eps)) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(approx (/ (+ (* (* x x) 1/2) -1) (neg eps)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 #s(approx (+ (* (* (* (* x -1/2) eps) (* (+ x eps) (- x eps))) (/ (neg eps) (neg (* eps eps)))) (* (- x eps) 1)) (neg.f64 eps)) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) #s(literal 1 binary64))) (.f64 (-.f64 x eps) (/.f64 (neg.f64 eps) (neg.f64 (.f64 eps eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

-12.6MiB live, 27.1MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify23.0ms (0.2%)

Memory

-5.5MiB live, 34.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	239
1	109	239

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 (+.f64 x eps) x) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 x eps) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

soundness1.0s (8.1%)

Memory

-5.0MiB live, 799.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458
0	379	4536
1	1191	4385
2	2934	4275
3	7112	4275
0	8306	3961
0	408	3712
1	1248	3510
2	3433	3428
0	8199	3203

Stop Event

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

Compiler

Compiled 226 to 167 computations (26.1% saved)

preprocess128.0ms (1%)

Memory: -1.9MiB live, 233.2MiB allocated
Compiler: Compiled 268 to 156 computations (41.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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%)

analyze44.0ms (0.4%)

sample7.2s (57.8%)

explain87.0ms (0.7%)

preprocess22.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize33.0ms (0.3%)

series5.0ms (0%)

simplify149.0ms (1.2%)

rewrite179.0ms (1.4%)

eval52.0ms (0.4%)

prune9.0ms (0.1%)

simplify201.0ms (1.6%)

localize251.0ms (2%)

series75.0ms (0.6%)

simplify165.0ms (1.3%)

rewrite151.0ms (1.2%)

eval136.0ms (1.1%)

prune24.0ms (0.2%)

simplify150.0ms (1.2%)

localize215.0ms (1.7%)

series46.0ms (0.4%)

simplify179.0ms (1.4%)

rewrite251.0ms (2%)

eval173.0ms (1.4%)

prune74.0ms (0.6%)

simplify141.0ms (1.1%)

localize266.0ms (2.1%)

series90.0ms (0.7%)

simplify223.0ms (1.8%)

rewrite305.0ms (2.5%)

eval162.0ms (1.3%)

prune64.0ms (0.5%)

regimes25.0ms (0.2%)

regimes30.0ms (0.2%)

regimes18.0ms (0.1%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0.1%)

regimes4.0ms (0%)

simplify23.0ms (0.2%)

soundness1.0s (8.1%)

preprocess128.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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