Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze43.0ms (0.3%)

Memory

-11.2MiB live, 69.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.7s (44.7%)

Memory

-147.1MiB live, 6 908.6MiB allocated

Samples

3.2s	26 569×	0	invalid
595.0ms	5 490×	0	valid
435.0ms	2 766×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

const: 693.0ms (22.2% of total)

ival-sin: 555.0ms (17.8% of total)

ival-<: 440.0ms (14.1% of total)

ival-mult: 275.0ms (8.8% of total)

ival-<=: 258.0ms (8.3% of total)

ival-add: 255.0ms (8.2% of total)

ival-fabs: 223.0ms (7.1% of total)

ival-sub: 185.0ms (5.9% of total)

ival-and: 105.0ms (3.4% of total)

adjust: 73.0ms (2.3% of total)

exact: 45.0ms (1.4% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

explain89.0ms (0.7%)

Memory

5.7MiB live, 203.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
219	3	(3.1424277155821244e-221 7.085516352255825e-224)	2	(-1.2352067758160804e-16 1.739936623971076e-18)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	0	-	1	(24.7591879775579 1.6096457297169295e-6)	`(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	220	6
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	217	2
-	3	34

Precision

0.9863636363636363

Recall

0.9908675799086758

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	217	2	0
-	3	4	30

Precision?

0.9690265486725663

Recall?

1.0

Freqs

test

number	freq
0	36
1	219
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms	182×	1	valid
16.0ms	326×	0	valid
1.0ms	4×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-sin: 13.0ms (48.1% of total)

adjust: 6.0ms (22.2% of total)

ival-sub: 5.0ms (18.5% of total)

ival-add: 3.0ms (11.1% of total)

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

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

preprocess29.0ms (0.2%)

Memory

-20.8MiB live, 58.2MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

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))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB 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))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize28.0ms (0.2%)

Memory

-19.9MiB live, 38.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.05688375946961356	(sin.f64 (+.f64 x eps))
accuracy	24.032844261011405	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

12.0ms	91×	1	valid
9.0ms	163×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 5.0ms (49.8% of total)

adjust: 2.0ms (19.9% of total)

ival-add: 2.0ms (19.9% of total)

ival-sub: 1.0ms (10% of total)

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

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

series4.0ms (0%)

Memory

5.2MiB live, 5.2MiB 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 (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 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 (* -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 (* 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 (+ 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 (- 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 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 (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 (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 (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 (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 (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 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt 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 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 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

21 calls:

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

simplify307.0ms (2.4%)

Memory

-5.6MiB live, 218.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite301.0ms (2.4%)

Memory

2.0MiB live, 200.1MiB allocated

Rules

4 986×	`lower-fma.f64`
4 986×	`lower-fma.f32`
4 676×	`lower-*.f64`
4 676×	`lower-*.f32`
2 176×	`lower-/.f64`

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

eval73.0ms (0.6%)

Memory: 0.6MiB live, 47.8MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune71.0ms (0.6%)

Memory

-8.7MiB live, 68.7MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	282	9	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	10	292

Accuracy

100.0%

Counts

292 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
▶	61.7%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
▶	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	61.7%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 297 to 178 computations (40.1% saved)

simplify322.0ms (2.5%)

Memory

7.5MiB live, 130.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
cost-diff	0	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
cost-diff	0	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff	0	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))

Rules

11 172×	`lower-fma.f32`
11 156×	`lower-fma.f64`
3 398×	`lower-*.f32`
3 380×	`lower-*.f64`
1 694×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	336
0	77	320
1	140	320
2	261	320
3	585	320
4	1222	320
5	2075	320
6	2740	320
7	3950	320
8	4464	320
9	5237	320
10	7054	320
11	7420	320
12	7575	320
13	7780	320
14	7786	320
0	8091	314

Stop Event

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

Calls

Call 1

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

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

localize217.0ms (1.7%)

Memory

29.6MiB live, 258.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(*.f64 x (cos.f64 eps))
accuracy	0.0078125	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
accuracy	23.841544050699547	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
accuracy	0.08984375	(.f64 x (.f64 x x))
accuracy	0.10546875	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
accuracy	0.830433265954673	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
accuracy	23.936665798204537	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
accuracy	0.05688375946961356	(sin.f64 (+.f64 x eps))
accuracy	0.08984375	(.f64 x (.f64 x x))
accuracy	1.0175437133369485	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	23.936665798204537	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
accuracy	0	(sin.f64 eps)
accuracy	1.7703210771148803	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0078125	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
accuracy	0.015625	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
accuracy	0.01953125	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
accuracy	0.34765625	(*.f64 eps #s(literal -1/6 binary64))

Samples

76.0ms	162×	0	valid
73.0ms	91×	1	valid
3.0ms	2×	3	valid
1.0ms	1×	5	exit

Compiler

Compiled 264 to 42 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 48.0ms (43.1% of total)

ival-sin: 21.0ms (18.9% of total)

ival-add: 13.0ms (11.7% of total)

const: 11.0ms (9.9% of total)

adjust: 8.0ms (7.2% of total)

ival-cos: 5.0ms (4.5% of total)

ival-sub: 3.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series77.0ms (0.6%)

Memory

-30.7MiB live, 54.0MiB allocated

Counts

21 → 408

Calls

Call 1

Inputs
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<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 (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) 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 #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x) (patch (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) (patch (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())

Outputs
#s(alt (sin eps) (taylor 0 x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.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 #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.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 #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) #<representation binary64>) () ())) ())
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#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* (pow eps 2) (cos x))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* (pow eps 2) (cos x))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/6 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2)))))))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/120 x) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 3)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 3)) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (* (pow eps 2) x))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x))))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x)))))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())

Calls

102 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))
2.0ms	x	@	0	(* x (+ (* (* x x) -1/5040) 1/120))
2.0ms	x	@	-inf	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))
1.0ms	eps	@	inf	(- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)
1.0ms	eps	@	0	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))

simplify326.0ms (2.6%)

Memory

14.3MiB live, 502.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 702×	`lower-fma.f64`
18 702×	`lower-fma.f32`
5 660×	`lower-+.f64`
5 660×	`lower-+.f32`
5 646×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	323	3889
1	1053	3788
2	3309	3761
0	8040	3455

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 397

Calls

Call 1

Inputs
(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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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))
(* 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)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 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))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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))
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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin 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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
(+ x (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(cos x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
x
(+ x (* -1/2 (* (pow eps 2) x)))
(+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))))
(+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x))))))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))
(* x (cos eps))

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (fma.f64 (sin.f64 eps) (.f64 x #s(literal -1/2 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) #s(literal -1 binary64))) (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))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.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 x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (.f64 eps eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (.f64 eps eps)))))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(.f64 (neg.f64 eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(.f64 (neg.f64 eps) (.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 x #s(literal 1/12 binary64)))) (.f64 x x) (.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 x x) #s(literal 1 binary64)))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (fma.f64 (sin.f64 eps) (.f64 x #s(literal -1/2 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) #s(literal -1 binary64))) (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))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(.f64 (.f64 x x) (-.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 eps)) x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 x x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (/.f64 (sin.f64 eps) x))) x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 x x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (/.f64 (sin.f64 eps) x))) x)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(fma.f64 eps (fma.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (fma.f64 x #s(literal 1/12 binary64) (.f64 eps #s(literal 1/24 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))) eps)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (cos.f64 eps)) x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (sin.f64 eps) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(.f64 x (.f64 x (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (cos.f64 eps) x))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (cos.f64 eps) x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (*.f64 x x)))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (cos.f64 eps) x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (*.f64 x x)))))
(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (sin.f64 eps) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(.f64 x (.f64 x (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (cos.f64 eps) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 x x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (+.f64 (cos.f64 eps) (/.f64 (sin.f64 eps) x)) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 x x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (+.f64 (cos.f64 eps) (/.f64 (sin.f64 eps) x)) x)))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(+ x (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)) x)
(+ x (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
(fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))) x)
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (cos.f64 eps)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(* -1/5040 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* -1/5040 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
x
(+ x (* -1/2 (* (pow eps 2) x)))
(fma.f64 eps (.f64 x (.f64 eps #s(literal -1/2 binary64))) x)
(+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))))
(fma.f64 eps (.f64 eps (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) x)
(+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x))))))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 x #s(literal -1/2 binary64))) x)
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))

rewrite292.0ms (2.3%)

Memory

-0.5MiB live, 481.6MiB allocated

Rules

6 174×	`lower-fma.f32`
6 158×	`lower-fma.f64`
4 812×	`lower-*.f32`
4 794×	`lower-*.f64`
3 624×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	240
0	77	230
1	298	230
2	2241	230
0	8886	230

Stop Event

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

Counts

21 → 360

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)))
(+.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)))) (/.f64 (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)))))
(fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 eps (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) eps (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (sin.f64 x) eps) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 (.f64 eps (cos.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps))))
(/.f64 (.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (.f64 eps (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64))) eps) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps) (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (.f64 eps (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))) (neg.f64 (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps)) (neg.f64 (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 x) eps)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps eps))))))
(.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(.f64 (fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) eps)
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(-.f64 (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) (/.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))))) (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))
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(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/128024064000 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (*.f64 x #s(literal 1/120 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64))))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x #s(literal 1/120 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/128024064000 binary64) #s(literal 1/1728000 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal -1/120 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/128024064000 binary64) #s(literal 1/1728000 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x)) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal -1/120 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/128024064000 binary64)))) (fma.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64))))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) x)
(*.f64 x (cos.f64 eps))
(*.f64 (cos.f64 eps) x)

eval128.0ms (1%)

Memory: 15.7MiB live, 165.9MiB allocated
Compiler: Compiled 26 541 to 1 605 computations (94% saved)

prune104.0ms (0.8%)

Memory

0.1MiB live, 197.4MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	856	12	868
Fresh	1	3	4
Picked	4	1	5
Done	0	1	1
Total	861	17	878

Accuracy

100.0%

Counts

878 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)) x)) x))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 x x) #s(literal 1 binary64))))))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
▶	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)))

Compiler

Compiled 599 to 349 computations (41.7% saved)

simplify189.0ms (1.5%)

Memory

-6.4MiB live, 148.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
cost-diff	0	(fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))))
cost-diff	0	(fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)))
cost-diff	0	(fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))
cost-diff	0	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

11 730×	`lower-fma.f32`
11 712×	`lower-fma.f64`
3 604×	`lower-*.f32`
3 576×	`lower-*.f64`
1 592×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	508
0	98	498
1	185	498
2	495	498
3	1363	494
4	2875	494
5	3467	494
6	4197	494
7	4958	494
8	5967	494
0	8057	473

Stop Event

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

Calls

Call 1

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

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

localize221.0ms (1.7%)

Memory

-19.7MiB live, 226.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
accuracy	0.01953125	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
accuracy	0.34765625	(*.f64 eps #s(literal -1/6 binary64))
accuracy	1.712134933360125	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
accuracy	0.125	(*.f64 x (+.f64 eps x))
accuracy	0.3046875	(*.f64 x #s(literal 1/12 binary64))
accuracy	0.34765625	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)))
accuracy	0.0078125	(fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
accuracy	0.17407461114818695	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
accuracy	23.841544050699547	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)
accuracy	0	(*.f64 eps #s(literal -1/2 binary64))
accuracy	0.00390625	(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)
accuracy	0.4726643395354717	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)))
accuracy	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.015625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04701630317403705	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

72.0ms	91×	1	valid
63.0ms	162×	0	valid
4.0ms	2×	3	valid
2.0ms	1×	5	exit

Compiler

Compiled 361 to 59 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 50.0ms (47.1% of total)

ival-add: 17.0ms (16% of total)

adjust: 12.0ms (11.3% of total)

ival-sin: 9.0ms (8.5% of total)

const: 7.0ms (6.6% of total)

ival-cos: 7.0ms (6.6% of total)

ival-sub: 3.0ms (2.8% of total)

exact: 1.0ms (0.9% of total)

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

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

series50.0ms (0.4%)

Memory

14.9MiB live, 51.7MiB allocated

Counts

26 → 552

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* eps (pow x 2))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/12 binary64)) (patch (.f64 x #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps x)) (taylor 0 x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps x)) (taylor 0 x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps x)) (taylor 0 x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps x) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps x) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps x) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ x (/ (pow x 2) eps))) (taylor inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ x (/ (pow x 2) eps))) (taylor inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ x (/ (pow x 2) eps))) (taylor inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())

Calls

138 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	(+ (* eps (* eps (+ (* x (* x 1/12)) -1/6))) (* -1/2 (* x (+ eps x))))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	0	(+ (* eps (+ (* eps (* eps (+ (* x (* x 1/12)) -1/6))) (* -1/2 (* x (+ eps x))))) eps)
1.0ms	eps	@	-inf	(+ (* eps (+ (* eps (* eps (+ (* x (* x 1/12)) -1/6))) (* -1/2 (* x (+ eps x))))) eps)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

simplify248.0ms (1.9%)

Memory

37.4MiB live, 259.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 036×	`lower-fma.f64`
10 036×	`lower-fma.f32`
6 432×	`lower-*.f64`
6 432×	`lower-*.f32`
2 704×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	525	6577
1	1682	6304
2	5059	6190
0	8171	5631

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 533

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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))))))))))
(* 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 (- (* 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)) (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))))))))
(* 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 (* -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))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
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(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(sin eps)
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(+ (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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
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(* (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)))
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(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* eps (+ 1 (* -1/2 (pow x 2))))
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(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
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(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
(+ x (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
eps
(+ eps x)
(+ eps (* x (+ 1 (* -1/2 (* eps x)))))
(+ eps (* x (+ 1 (* -1/2 (* eps x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/2 eps) (+ (/ 1 x) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (/ 1 x) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ eps x)) 1) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ eps x)) 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) 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 (- (* 1/12 (pow x 2)) 1/6)))))))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)))))
(+ eps (* -1/6 (pow eps 3)))
(+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))
(+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* -1/6 (/ (pow eps 3) (pow x 2))) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ eps (pow x 2))))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* -1/6 (/ (pow eps 3) (pow x 2))) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ eps (pow x 2))))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1/6 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))
(+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
(+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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))
(* 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)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 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))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(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))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* -1/6 eps)
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* eps x)
(* x (+ eps x))
(* x (+ eps x))
(* x (+ eps x))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(* eps x)
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)

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

rewrite298.0ms (2.3%)

Memory

-31.6MiB live, 331.5MiB allocated

Rules

4 368×	`lower-fma.f32`
4 350×	`lower-fma.f64`
3 786×	`lower-/.f64`
3 786×	`lower-/.f32`
3 750×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	429
0	98	421
1	375	421
2	3500	421
0	8503	414

Stop Event

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

Counts

26 → 536

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 eps #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) eps #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (*.f64 eps eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (neg.f64 (.f64 eps (.f64 eps eps)))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 eps #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) eps)
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))))
(/.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
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(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (.f64 x x) #s(literal -1/72 binary64))) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (*.f64 x x) #s(literal -1/72 binary64))) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/6 binary64)) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/6 binary64)) eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/216 binary64)))) (neg.f64 (fma.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64))) (-.f64 (.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 eps #s(literal -1/6 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64)))) (.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal -1/6 binary64))))) (neg.f64 (-.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 eps #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (*.f64 x x) #s(literal -1/72 binary64)))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64)))) (neg.f64 (.f64 eps (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (*.f64 x x) #s(literal -1/72 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64)))) (neg.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64)) eps)) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (*.f64 x x) #s(literal -1/72 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64)) eps)) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/6 binary64))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps)
(*.f64 x #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) x)
(+.f64 (.f64 x x) (.f64 x eps))
(+.f64 (.f64 x eps) (.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x eps) (.f64 x x))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 x eps) (.f64 x x))))
(fma.f64 x x (*.f64 x eps))
(fma.f64 x eps (*.f64 x x))
(fma.f64 eps x (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x eps))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x eps))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (fma.f64 (.f64 x x) (.f64 eps eps) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x eps) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x eps) (.f64 x x)))
(/.f64 (.f64 x (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 x (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 x (.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 x (.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) x) (-.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) x) (-.f64 eps x))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (fma.f64 (.f64 x x) (.f64 eps eps) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x eps) (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x)))) (neg.f64 (-.f64 (.f64 x eps) (.f64 x x))))
(/.f64 (neg.f64 (.f64 x (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 x (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 x (.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (.f64 x (.f64 (+.f64 x eps) (-.f64 eps x)))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) x)) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) x)) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) x)) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) x)) (neg.f64 (-.f64 eps x)))
(*.f64 x (+.f64 x eps))
(*.f64 (+.f64 x eps) x)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (neg.f64 eps))
(/.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64)) (.f64 eps eps))
(/.f64 (neg.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64))) (neg.f64 (.f64 eps eps)))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)

eval136.0ms (1.1%)

Memory: 22.4MiB live, 244.3MiB allocated
Compiler: Compiled 28 851 to 2 121 computations (92.6% saved)

prune167.0ms (1.3%)

Memory

-37.9MiB live, 318.4MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 055	14	1 069
Fresh	7	3	10
Picked	4	1	5
Done	1	1	2
Total	1 067	19	1 086

Accuracy

100.0%

Counts

1 086 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
✓	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
	37.7%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (.f64 (.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))))) x))
▶	61.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
▶	37.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) x eps)))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* x (* x 1/12)) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))) eps)))
	36.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))))
▶	56.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))))))

Compiler

Compiled 667 to 327 computations (51% saved)

simplify273.0ms (2.1%)

Memory

34.4MiB live, 269.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
cost-diff	0	(.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
cost-diff	3904	(.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))))
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
cost-diff	320	(.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))))
cost-diff	704	(.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
cost-diff	0	#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
cost-diff	0	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
cost-diff	0	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

12 986×	`lower-fma.f32`
12 974×	`lower-fma.f64`
5 096×	`lower-*.f32`
5 072×	`lower-*.f64`
1 484×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	829
0	95	849
1	186	839
2	440	677
3	1097	660
4	2429	660
5	4741	660
0	8276	625

Stop Event

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

Calls

Call 1

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

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

localize209.0ms (1.6%)

Memory

-28.7MiB live, 288.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.25	(/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
accuracy	23.937722513506415	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)
accuracy	27.102553663868125	(.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))))
accuracy	0.28515625	(.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))))
accuracy	0.4726643395354717	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
accuracy	25.776105627115033	(/.f64 eps (*.f64 x x))
accuracy	0.01171875	(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)
accuracy	0.125	(*.f64 x (+.f64 eps x))
accuracy	0.14377293255696966	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
accuracy	0.17407461114818695	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
accuracy	0.6071230741719903	#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
accuracy	1.0802580118509608	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
accuracy	23.937722513506415	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
accuracy	0.0078125	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
accuracy	0.015625	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04701630317403705	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.34765625	(*.f64 eps #s(literal -1/48 binary64))

Samples

64.0ms	92×	1	valid
62.0ms	159×	0	valid
8.0ms	4×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 455 to 58 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-mult: 44.0ms (40.9% of total)

ival-add: 20.0ms (18.6% of total)

adjust: 12.0ms (11.2% of total)

ival-sin: 11.0ms (10.2% of total)

ival-cos: 8.0ms (7.4% of total)

ival-div: 5.0ms (4.6% of total)

const: 4.0ms (3.7% of total)

ival-sub: 3.0ms (2.8% of total)

exact: 1.0ms (0.9% of total)

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

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

series72.0ms (0.6%)

Memory

19.1MiB live, 55.4MiB allocated

Counts

27 → 600

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x) (taylor -inf eps) (#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x) (patch (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x) (taylor -inf eps) (#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x) (patch (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x) (taylor -inf eps) (#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x) (patch (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x) (taylor -inf eps) (#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x) (patch (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin eps)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* 1/2 (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (sin eps))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -2 (* (pow x 2) (sin eps))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (+ (* 4 (/ 1 (sin eps))) (* 8 (/ (pow (+ 1 (cos eps)) 2) (pow (sin eps) 3)))) (pow x 2))) (+ (* 4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps))))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (+ (* 2 (/ (* (+ 1 (cos eps)) (+ (* 8 (/ (pow (+ 1 (cos eps)) 2) (pow (sin eps) 3))) (* 4 (/ 1 (sin eps))))) (sin eps))) (* 8 (/ (+ 1 (cos eps)) (pow (sin eps) 2)))) (pow x 3))) (+ (* 4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (+ (* 8 (/ (pow (+ 1 (cos eps)) 2) (* (pow x 2) (pow (sin eps) 3)))) (+ (* 2 (/ 1 (sin eps))) (* 4 (/ 1 (* (pow x 2) (sin eps)))))))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -2 (* (pow x 2) (sin eps))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 4 (/ (- (* -1 (cos eps)) 1) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (+ (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (* x (pow (sin eps) 3)))) (/ 4 (* x (sin eps)))) (* 4 (/ (- (* -1 (cos eps)) 1) (pow (sin eps) 2)))) x)) (* 2 (/ 1 (sin eps)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (+ (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (pow (sin eps) 3))) (* 4 (/ 1 (sin eps)))) (- (* -1 (cos eps)) 1)) (* x (sin eps)))) (* 8 (/ (- (* -1 (cos eps)) 1) (* x (pow (sin eps) 2))))) (+ (* 4 (/ 1 (sin eps))) (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (pow (sin eps) 3))))) x)) (* 4 (/ (- (* -1 (cos eps)) 1) (pow (sin eps) 2)))) x)) (* 2 (/ 1 (sin eps)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (/ (* eps (+ 1 (* -1/2 (pow x 2)))) (pow x 2))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (* eps (- (* 1/8 (/ 1 x)) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) (* 1/4 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/24 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))) (+ (* 1/16 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))) (* 1/2 (/ (* (+ 1 (* -1/2 (pow x 2))) (- (* 1/8 (/ 1 x)) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) x)))))) (* 1/8 (/ 1 x))) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) (* 1/4 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())

Calls

150 calls:

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

simplify411.0ms (3.2%)

Memory

-10.2MiB live, 301.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 158×	`lower-fma.f64`
12 158×	`lower-fma.f32`
6 000×	`lower-*.f64`
6 000×	`lower-*.f32`
4 672×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	665	8166
1	2200	7749
2	7049	7707
0	8216	7114

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 592

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (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))))))))))
(* 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 (- (* 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)) (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))))))))
(* 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 (* -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))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin 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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (/ (cos eps) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
(+ x (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
(+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))
x
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ x (* eps (+ 1 (* -1/2 (pow x 2)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (/ x eps))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1 (* -1/2 (pow x 2)))) (* -1 (/ x eps)))))
eps
(+ eps x)
(+ eps (* x (+ 1 (* -1/2 (* eps x)))))
(+ eps (* x (+ 1 (* -1/2 (* eps x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/2 eps) (+ (/ 1 x) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (/ 1 x) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ eps x)) 1) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ eps x)) 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) 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)))))
(* -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))))
(* -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)))
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 (* 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 (* 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 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(* -1 (* eps (* (pow x 2) (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* (pow x 2) (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* (pow x 2) (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* (pow x 2) (- 1/2 (/ 1 (pow x 2))))))
(/ eps x)
(/ (+ eps (* -1/2 (* eps (pow x 2)))) x)
(/ (+ eps (* -1/2 (* eps (pow x 2)))) x)
(/ (+ eps (* -1/2 (* eps (pow x 2)))) x)
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ eps (pow x 2))))
(* x (+ (* -1/2 eps) (/ eps (pow x 2))))
(* x (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps x))
(* -1 (* x (+ (* -1 (/ eps (pow x 2))) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ eps (pow x 2))) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ eps (pow x 2))) (* 1/2 eps))))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* eps (* x (- (/ 1 (pow x 2)) 1/2)))
(* -1 (* eps (* x (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* x (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* x (- 1/2 (/ 1 (pow x 2))))))
(* -1 (* eps (* x (- 1/2 (/ 1 (pow x 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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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)
(+ (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)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 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) (* -1/2 (* x (sin eps)))) 1)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps 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) (* -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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (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))
(pow (sin eps) 2)
(+ (* x (+ (* (sin eps) (+ 1 (cos eps))) (* (sin eps) (- (cos eps) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* x (+ (* -1 (pow (sin eps) 2)) (* (+ 1 (cos eps)) (- (cos eps) 1)))) (+ (* (sin eps) (+ 1 (cos eps))) (* (sin eps) (- (cos eps) 1))))) (pow (sin eps) 2))
(+ (* x (+ (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1/2 (* (sin eps) (+ 1 (cos eps)))) (* -1/2 (* (sin eps) (- (cos eps) 1))))) (* (+ 1 (cos eps)) (- (cos eps) 1))))) (+ (* (sin eps) (+ 1 (cos eps))) (* (sin eps) (- (cos eps) 1))))) (pow (sin eps) 2))
(* 1/4 (* (pow x 4) (pow (sin eps) 2)))
(* (pow x 4) (+ (* -1/2 (/ (* (sin eps) (+ 1 (cos eps))) x)) (+ (* -1/2 (/ (* (sin eps) (- (cos eps) 1)) x)) (* 1/4 (pow (sin eps) 2)))))
(* (pow x 4) (+ (* -1 (/ (pow (sin eps) 2) (pow x 2))) (+ (* -1/2 (/ (* (sin eps) (+ 1 (cos eps))) x)) (+ (* -1/2 (/ (* (sin eps) (- (cos eps) 1)) x)) (+ (* 1/4 (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (cos eps) 1)) (pow x 2)))))))
(* (pow x 4) (+ (* -1 (/ (pow (sin eps) 2) (pow x 2))) (+ (* -1/2 (/ (* (sin eps) (+ 1 (cos eps))) x)) (+ (* -1/2 (/ (* (sin eps) (- (cos eps) 1)) x)) (+ (* 1/4 (pow (sin eps) 2)) (+ (/ (* (sin eps) (+ 1 (cos eps))) (pow x 3)) (+ (/ (* (sin eps) (- (cos eps) 1)) (pow x 3)) (/ (* (+ 1 (cos eps)) (- (cos eps) 1)) (pow x 2)))))))))
(* 1/4 (* (pow x 4) (pow (sin eps) 2)))
(* (pow x 4) (+ (* -1 (/ (+ (* -1/2 (* (sin eps) (+ 1 (* -1 (cos eps))))) (* -1/2 (* (sin eps) (- (* -1 (cos eps)) 1)))) x)) (* 1/4 (pow (sin eps) 2))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* (+ 1 (* -1 (cos eps))) (- (* -1 (cos eps)) 1))) x)) (+ (* -1/2 (* (sin eps) (+ 1 (* -1 (cos eps))))) (* -1/2 (* (sin eps) (- (* -1 (cos eps)) 1))))) x)) (* 1/4 (pow (sin eps) 2))))
(* (pow x 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (sin eps) (+ 1 (* -1 (cos eps)))) (* (sin eps) (- (* -1 (cos eps)) 1))) x)) (+ (* -1 (pow (sin eps) 2)) (* (+ 1 (* -1 (cos eps))) (- (* -1 (cos eps)) 1)))) x)) (+ (* -1/2 (* (sin eps) (+ 1 (* -1 (cos eps))))) (* -1/2 (* (sin eps) (- (* -1 (cos eps)) 1))))) x)) (* 1/4 (pow (sin eps) 2))))
(* 2 (* eps (* x (+ 1 (* -1/2 (pow x 2))))))
(* eps (+ (* 2 (* x (+ 1 (* -1/2 (pow x 2))))) (* eps (+ (* -1 (pow x 2)) (pow (+ 1 (* -1/2 (pow x 2))) 2)))))
(* eps (+ (* 2 (* x (+ 1 (* -1/2 (pow x 2))))) (* eps (+ (* -1 (pow x 2)) (+ (* eps (+ (* -1 (* x (+ 1 (* -1/2 (pow x 2))))) (* -1/3 (* x (+ 1 (* -1/2 (pow x 2))))))) (pow (+ 1 (* -1/2 (pow x 2))) 2))))))
(* eps (+ (* 2 (* x (+ 1 (* -1/2 (pow x 2))))) (* eps (+ (* -1 (pow x 2)) (+ (* eps (+ (* -1 (* x (+ 1 (* -1/2 (pow x 2))))) (+ (* -1/3 (* x (+ 1 (* -1/2 (pow x 2))))) (* eps (+ (* -1/3 (pow (+ 1 (* -1/2 (pow x 2))) 2)) (+ (* 1/12 (pow x 2)) (* 1/4 (pow x 2)))))))) (pow (+ 1 (* -1/2 (pow x 2))) 2))))))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(* (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))) (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x))
(sin eps)
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ 1 x) (/ (cos eps) x))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ 1 x) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2))))))
(* (pow x 2) (+ (* -1/2 (sin eps)) (+ (/ 1 x) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2))))))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (cos eps)) 1) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (- (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) 1) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (- (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x))) 1) x)) (* -1/2 (sin eps))))
(* 2 x)
(+ (* 2 x) (* eps (+ 1 (* -1/2 (pow x 2)))))
(+ (* 2 x) (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
(+ (* 2 x) (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(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))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* eps x)
(* x (+ eps x))
(* x (+ eps x))
(* x (+ eps x))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(* eps x)
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 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) (* -1/2 (* x (sin eps)))) 1)))
(* -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 (* (pow x 2) (sin eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))
(* 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) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)
(/ 1 (sin eps))
(+ (* -1 (* x (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* 1/2 (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (sin eps))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))
(/ -2 (* (pow x 2) (sin eps)))
(/ (- (* -4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps)))) (pow x 2))
(/ (- (* -1 (/ (+ (* 4 (/ 1 (sin eps))) (* 8 (/ (pow (+ 1 (cos eps)) 2) (pow (sin eps) 3)))) (pow x 2))) (+ (* 4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps))))) (pow x 2))
(/ (- (* -1 (/ (+ (* 2 (/ (* (+ 1 (cos eps)) (+ (* 8 (/ (pow (+ 1 (cos eps)) 2) (pow (sin eps) 3))) (* 4 (/ 1 (sin eps))))) (sin eps))) (* 8 (/ (+ 1 (cos eps)) (pow (sin eps) 2)))) (pow x 3))) (+ (* 4 (/ (+ 1 (cos eps)) (* x (pow (sin eps) 2)))) (+ (* 8 (/ (pow (+ 1 (cos eps)) 2) (* (pow x 2) (pow (sin eps) 3)))) (+ (* 2 (/ 1 (sin eps))) (* 4 (/ 1 (* (pow x 2) (sin eps)))))))) (pow x 2))
(/ -2 (* (pow x 2) (sin eps)))
(/ (- (* 4 (/ (- (* -1 (cos eps)) 1) (* x (pow (sin eps) 2)))) (* 2 (/ 1 (sin eps)))) (pow x 2))
(/ (- (* -1 (/ (- (+ (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (* x (pow (sin eps) 3)))) (/ 4 (* x (sin eps)))) (* 4 (/ (- (* -1 (cos eps)) 1) (pow (sin eps) 2)))) x)) (* 2 (/ 1 (sin eps)))) (pow x 2))
(/ (- (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (+ (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (pow (sin eps) 3))) (* 4 (/ 1 (sin eps)))) (- (* -1 (cos eps)) 1)) (* x (sin eps)))) (* 8 (/ (- (* -1 (cos eps)) 1) (* x (pow (sin eps) 2))))) (+ (* 4 (/ 1 (sin eps))) (* 8 (/ (pow (- (* -1 (cos eps)) 1) 2) (pow (sin eps) 3))))) x)) (* 4 (/ (- (* -1 (cos eps)) 1) (pow (sin eps) 2)))) x)) (* 2 (/ 1 (sin eps)))) (pow x 2))
(/ 1/2 x)
(+ (* -1/4 (/ (* eps (+ 1 (* -1/2 (pow x 2)))) (pow x 2))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* eps (- (* 1/8 (/ 1 x)) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) (* 1/4 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/24 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))) (+ (* 1/16 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))) (* 1/2 (/ (* (+ 1 (* -1/2 (pow x 2))) (- (* 1/8 (/ 1 x)) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) x)))))) (* 1/8 (/ 1 x))) (* -1/8 (/ (pow (+ 1 (* -1/2 (pow x 2))) 2) (pow x 3))))) (* 1/4 (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))))) (* 1/2 (/ 1 x)))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 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 (* 2 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 (* 2 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 (* 2 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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal -2 binary64))))
(+ (* 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))))))))
(fma.f64 x (fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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))))))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 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 (* 2 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 (* 2 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 (* 2 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 (* -2 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 (* -2 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 (* -2 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 (* -2 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)))
(* 1/2 (* eps (cos x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (-.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64))) (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))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.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 x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
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(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 eps) (fma.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 eps) (fma.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 eps) (fma.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 eps) (fma.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))
(/ 1 (+ x (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 eps) (fma.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))

rewrite373.0ms (2.9%)

Memory

29.2MiB live, 256.5MiB allocated

Rules

5 684×	`lower-*.f32`
5 660×	`lower-*.f64`
3 938×	`lower-fma.f32`
3 926×	`lower-fma.f64`
3 400×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	720
0	95	738
1	410	547
2	3352	547
0	8876	530

Stop Event

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

Counts

27 → 430

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 (neg.f64 eps) eps))) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) x))
(+.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (neg.f64 x))
(+.f64 (neg.f64 x) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) x)
(-.f64 (/.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))))))
(-.f64 (/.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))) (/.f64 (.f64 x x) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))))
(fma.f64 #s(literal -1 binary64) x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))) (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (neg.f64 (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) x))))
(/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))))))
(/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (-.f64 (.f64 x x) (.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) (neg.f64 x)))))
(/.f64 (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps))) x)) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 x eps)))))
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(.f64 (/.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (.f64 x (.f64 x x)))) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x) (.f64 x x)))
(.f64 (/.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
(exp.f64 (.f64 (log.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))))
(pow.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal -1 binary64))
(pow.f64 (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))))
(.f64 (pow.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (.f64 x (.f64 x x)))) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (.f64 x (.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x) (.f64 x x))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))) #s(literal -1 binary64)))

eval223.0ms (1.8%)

Memory: -8.8MiB live, 162.2MiB allocated
Compiler: Compiled 31 892 to 1 891 computations (94.1% saved)

prune214.0ms (1.7%)

Memory

8.6MiB live, 169.0MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	1 060	11	1 071
Fresh	1	11	12
Picked	4	1	5
Done	0	2	2
Total	1 065	25	1 090

Accuracy

100.0%

Counts

1 090 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	37.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	56.4%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
✓	61.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
	37.7%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (.f64 (.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))))) x))
✓	61.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
	25.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) #s(approx (/ 1 (+ x (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))))) (/.f64 #s(literal 1/2 binary64) x))))
	25.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
	55.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 eps (fma.f64 eps (.f64 (+.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 x (.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
	34.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 #s(literal 2 binary64) (.f64 x (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)))))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x (+.f64 x eps)) eps) #s(literal -1/2 binary64) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) x eps)))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) #s(approx ( x (+ eps x)) (*.f64 eps x)) eps)))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* x (* x 1/12)) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))) eps)))
	36.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps x)) x))))

Compiler

Compiled 1 388 to 446 computations (67.9% saved)

regimes63.0ms (0.5%)

Memory

-6.8MiB live, 34.5MiB allocated

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) #s(approx ( x (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x (+.f64 x eps)) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* x (* x 1/12)) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 x x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) #s(approx (/ 1 (+ x (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))))) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 #s(literal 2 binary64) (.f64 x (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (.f64 (.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))))) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 eps (fma.f64 eps (.f64 (+.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 x (.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))

Outputs

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

Calls

3 calls:

37.0ms	eps
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	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 15 to 10 computations (33.3% saved)

regimes48.0ms (0.4%)

Memory

9.4MiB live, 47.0MiB allocated

Counts

46 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) #s(approx ( x (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 (.f64 x (+.f64 x eps)) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* x (* x 1/12)) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* (* eps -1/2) (* x x)) eps) (.f64 x (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 x x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) #s(approx (/ 1 (+ x (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))))) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 #s(literal 2 binary64) (.f64 x (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (.f64 (.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))) (-.f64 eps x))))) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx ( (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)) (.f64 eps (fma.f64 eps (.f64 (+.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) (-.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 x (.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

22.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x
12.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes53.0ms (0.4%)

Memory

-11.3MiB live, 63.3MiB allocated

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

30.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x
9.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.3%)

Memory

1.2MiB live, 43.5MiB allocated

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	eps
8.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

16.4MiB live, 54.0MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-3.6MiB live, 33.7MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-2.0MiB live, 35.8MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-36.9MiB live, 19.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(approx (* x (+ 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
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Accuracy

Total -36.2b remaining (-146.5%)

Threshold costs -36.2b (-146.5%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
61.4%	1	`x`
61.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
61.4%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	336
1	120	336
2	124	336
3	126	336
4	127	336

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (9.2%)

Memory

17.1MiB live, 962.3MiB allocated

Rules

18 702×	`lower-fma.f64`
18 702×	`lower-fma.f32`
16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
12 158×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	665	8166
1	2200	7749
2	7049	7707
0	8216	7114
0	525	6577
1	1682	6304
2	5059	6190
0	8171	5631
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	323	3889
1	1053	3788
2	3309	3761
0	8040	3455

Stop Event

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

Compiler

Compiled 265 to 142 computations (46.4% saved)

preprocess83.0ms (0.7%)

Memory: 0.3MiB live, 237.5MiB allocated
Compiler: Compiled 388 to 174 computations (55.2% 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%)

analyze43.0ms (0.3%)

sample5.7s (44.7%)

explain89.0ms (0.7%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize28.0ms (0.2%)

series4.0ms (0%)

simplify307.0ms (2.4%)

rewrite301.0ms (2.4%)

eval73.0ms (0.6%)

prune71.0ms (0.6%)

simplify322.0ms (2.5%)

localize217.0ms (1.7%)

series77.0ms (0.6%)

simplify326.0ms (2.6%)

rewrite292.0ms (2.3%)

eval128.0ms (1%)

prune104.0ms (0.8%)

simplify189.0ms (1.5%)

localize221.0ms (1.7%)

series50.0ms (0.4%)

simplify248.0ms (1.9%)

rewrite298.0ms (2.3%)

eval136.0ms (1.1%)

prune167.0ms (1.3%)

simplify273.0ms (2.1%)

localize209.0ms (1.6%)

series72.0ms (0.6%)

simplify411.0ms (3.2%)

rewrite373.0ms (2.9%)

eval223.0ms (1.8%)

prune214.0ms (1.7%)

regimes63.0ms (0.5%)

regimes48.0ms (0.4%)

regimes53.0ms (0.4%)

regimes33.0ms (0.3%)

regimes27.0ms (0.2%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes14.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

simplify10.0ms (0.1%)

soundness1.2s (9.2%)

preprocess83.0ms (0.7%)

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