Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze55.0ms (0.4%)

Memory

-7.3MiB live, 96.4MiB 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)

sample6.1s (47.6%)

Memory

-273.7MiB live, 7 432.9MiB allocated

Samples

3.3s	26 007×	0	invalid
736.0ms	5 482×	0	valid
568.0ms	2 774×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.2s

const: 729.0ms (22.5% of total)

ival-sin: 702.0ms (21.7% of total)

ival-<=: 355.0ms (11% of total)

ival-mult: 264.0ms (8.2% of total)

ival-<: 252.0ms (7.8% of total)

ival-add: 245.0ms (7.6% of total)

ival-fabs: 241.0ms (7.5% of total)

ival-sub: 214.0ms (6.6% of total)

ival-and: 98.0ms (3% of total)

adjust: 75.0ms (2.3% of total)

exact: 47.0ms (1.5% of total)

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

Bogosity

explain90.0ms (0.7%)

Memory

14.7MiB live, 176.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
232	2	(-2.0551155756050403e-128 1.3249092854559037e-130)	4	(1.1885620577001862e-305 2.916540752734288e-307)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	230	7
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	228	4
-	2	22

Precision

0.991304347826087

Recall

0.9827586206896551

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	228	4	0
-	2	3	19

Precision?

0.9789029535864979

Recall?

1.0

Freqs

test

number	freq
0	26
1	229
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

20.0ms	336×	0	valid
18.0ms	176×	1	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 9.0ms (47.4% of total)

adjust: 3.0ms (15.8% of total)

ival-sub: 3.0ms (15.8% of total)

ival-add: 3.0ms (15.8% of total)

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

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

preprocess27.0ms (0.2%)

Memory

1.5MiB live, 38.4MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

-27.0MiB live, 17.8MiB 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)

localize25.0ms (0.2%)

Memory

17.2MiB live, 56.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.04906380013364235	(sin.f64 (+.f64 x eps))
accuracy	24.270829502370006	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	88×	1	valid
8.0ms	168×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 4.0ms (37.4% of total)

adjust: 3.0ms (28.1% of total)

ival-add: 2.0ms (18.7% of total)

ival-sub: 1.0ms (9.4% of total)

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

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

series4.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (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	x	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)

simplify243.0ms (1.9%)

Memory

15.9MiB live, 205.4MiB 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)

rewrite328.0ms (2.6%)

Memory

-10.4MiB live, 244.9MiB 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))

eval131.0ms (1%)

Memory: -8.4MiB live, 63.2MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune62.0ms (0.5%)

Memory

-18.9MiB live, 69.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	5	292

Accuracy

100.0%

Counts

292 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.7%	(-.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))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 118 to 74 computations (37.3% saved)

simplify259.0ms (2%)

Memory

9.3MiB live, 167.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

7 710×	`lower-fma.f32`
7 704×	`lower-fma.f64`
4 884×	`lower-*.f32`
4 866×	`lower-*.f64`
1 562×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	199
0	61	181
1	96	181
2	183	181
3	306	177
4	388	177
5	602	177
6	1693	177
7	2042	177
8	2175	177
9	2211	177
10	2313	177
11	2482	177
12	3224	177
13	3467	177
14	3749	177
15	3990	177
16	4400	177
17	6290	177
0	8006	173

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

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

localize127.0ms (1%)

Memory

27.6MiB live, 144.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
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	0.0078125	(.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	0.03602182469244065	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.04906380013364235	(sin.f64 (+.f64 x eps))
accuracy	0.09375	(.f64 x (.f64 x x))
accuracy	0.5636859616960324	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	24.270829502370006	(-.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	(cos.f64 x)
accuracy	0.00390625	(*.f64 eps (cos.f64 x))
accuracy	0.14669107811679954	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
accuracy	0	(sin.f64 eps)
accuracy	0.9831214042044314	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
accuracy	0.0078125	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
accuracy	0.012382519536884034	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))

Samples

37.0ms	168×	0	valid
33.0ms	88×	1	valid

Compiler

Compiled 172 to 33 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 19.0ms (39.4% of total)

ival-sin: 8.0ms (16.6% of total)

ival-add: 7.0ms (14.5% of total)

adjust: 5.0ms (10.4% of total)

ival-cos: 4.0ms (8.3% of total)

const: 4.0ms (8.3% of total)

ival-sub: 2.0ms (4.1% of total)

exact: 1.0ms (2.1% of total)

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

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

series51.0ms (0.4%)

Memory

-31.0MiB live, 38.6MiB allocated

Counts

20 → 396

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

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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (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)) (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)) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (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)) (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)) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (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)) (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)) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (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)) (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)) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (sin x))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (sin x))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ eps (* -1/2 (* (pow eps 2) x))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (taylor inf x) (#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 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (taylor inf x) (#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 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (taylor inf x) (#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 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (taylor inf x) (#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 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) (taylor -inf x) (#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 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) (taylor -inf x) (#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 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) (taylor -inf x) (#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 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) (taylor -inf x) (#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 (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 (cos (* 1/2 eps)) (taylor 0 x) (#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 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) (taylor 0 x) (#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 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) (taylor 0 x) (#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 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) (taylor 0 x) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#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 (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#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 (cos x) (taylor 0 eps) (#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 (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#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 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) (taylor 0 eps) (#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 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) (taylor 0 eps) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#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 (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#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 (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#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 (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#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 (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#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 (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#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 (* 1/2 eps) (taylor 0 eps) (#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 (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#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 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#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 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#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 (sin (* 1/2 eps)) (taylor inf eps) (#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 (sin (* 1/2 eps)) (taylor inf eps) (#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 (sin (* 1/2 eps)) (taylor inf eps) (#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 (sin (* 1/2 eps)) (taylor inf eps) (#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 (sin (* 1/2 eps)) (taylor -inf eps) (#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 (sin (* 1/2 eps)) (taylor -inf eps) (#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 (sin (* 1/2 eps)) (taylor -inf eps) (#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 (sin (* 1/2 eps)) (taylor -inf eps) (#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>) () ())) ())

Calls

99 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	eps	@	0	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
1.0ms	x	@	0	(* -1/2 (sin x))
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))

simplify357.0ms (2.8%)

Memory

-16.3MiB live, 298.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 684×	`lower-fma.f64`
13 684×	`lower-fma.f32`
6 158×	`lower-*.f64`
6 158×	`lower-*.f32`
3 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	3321
1	1096	3209
2	2836	3169
3	6540	3169
0	8160	2921

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 371

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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -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))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos 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)))
(+ (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)
(* 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)))
(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)
(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))

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

rewrite484.0ms (3.8%)

Memory

-12.4MiB live, 384.5MiB allocated

Rules

6 010×	`lower-fma.f32`
6 004×	`lower-fma.f64`
4 252×	`lower-/.f64`
4 252×	`lower-/.f32`
4 168×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	161
0	61	147
1	189	147
2	1458	147
0	8238	147

Stop Event

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

Counts

20 → 625

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

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

eval154.0ms (1.2%)

Memory: 31.8MiB live, 145.6MiB allocated
Compiler: Compiled 24 311 to 2 222 computations (90.9% saved)

prune181.0ms (1.4%)

Memory

-12.8MiB live, 190.8MiB allocated

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	998	11	1 009
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 001	13	1 014

Accuracy

100.0%

Counts

1 014 → 13

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))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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))
▶	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	55.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.8%	#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))) (cos.f64 x))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 366 to 210 computations (42.6% saved)

simplify213.0ms (1.7%)

Memory

13.6MiB live, 127.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 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))) (cos.f64 x))
cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 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))) (cos.f64 x))))
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
cost-diff	0	(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
cost-diff	0	(.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 (cos.f64 x) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
cost-diff	6400	(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 (cos.f64 x) #s(literal 1/2 binary64)))

Rules

7 702×	`lower-fma.f32`
7 690×	`lower-fma.f64`
4 618×	`lower-*.f32`
4 594×	`lower-*.f64`
2 074×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	413
0	85	409
1	160	409
2	439	409
3	822	405
4	1064	405
5	1538	405
6	2414	405
7	2510	405
8	2703	405
9	3158	405
10	4381	405
11	5946	405
12	7323	405
0	8220	393

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64)))))
(.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 (cos.f64 x) #s(literal 1/2 binary64))))
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 (cos.f64 x) #s(literal 1/2 binary64)))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))
(*.f64 (cos.f64 x) #s(literal -1/12 binary64))
(cos.f64 x)
x
#s(literal -1/12 binary64)
(*.f64 (sin.f64 x) #s(literal -1/4 binary64))
(sin.f64 x)
#s(literal -1/4 binary64)
(*.f64 (cos.f64 x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(+.f64 eps x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 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))) (cos.f64 x))))
(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
eps
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 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)
(cos.f64 x)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps (fma.f64 (cos.f64 x) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps (fma.f64 (cos.f64 x) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(.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 (cos.f64 x) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 (cos.f64 x) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
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 (cos.f64 x) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 x) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))
(*.f64 (cos.f64 x) #s(literal -1/12 binary64))
(cos.f64 x)
x
#s(literal -1/12 binary64)
(*.f64 (sin.f64 x) #s(literal -1/4 binary64))
(sin.f64 x)
#s(literal -1/4 binary64)
(*.f64 (cos.f64 x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (cos.f64 x))
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(+.f64 eps x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 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))) (cos.f64 x))))
(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
eps
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 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)
(cos.f64 x)

localize175.0ms (1.4%)

Memory

5.9MiB live, 244.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))
accuracy	0.0078125	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
accuracy	0.012382519536884034	#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))) (cos.f64 x))))
accuracy	0.9039078615296754	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
accuracy	0.00390625	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
accuracy	0.14669107811679954	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
accuracy	0.31640625	(*.f64 x #s(literal 1/24 binary64))
accuracy	0.4698620761962506	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	0.0078125	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))
accuracy	0.012382519536884034	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
accuracy	0.5725825466978471	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))
accuracy	0.0078125	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
accuracy	0.012382519536884034	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
accuracy	0.9955067337395535	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64)))))
accuracy	0.00390625	(.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 (cos.f64 x) #s(literal 1/2 binary64))))
accuracy	0.0078125	(fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))
accuracy	0.01171875	(*.f64 (cos.f64 x) #s(literal -1/12 binary64))

Samples

64.0ms	89×	1	valid
57.0ms	167×	0	valid

Compiler

Compiled 263 to 49 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-mult: 40.0ms (49.9% of total)

ival-add: 12.0ms (15% of total)

adjust: 8.0ms (10% of total)

const: 7.0ms (8.7% of total)

ival-sin: 6.0ms (7.5% of total)

ival-cos: 4.0ms (5% of total)

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

exact: 1.0ms (1.2% of total)

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

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

series35.0ms (0.3%)

Memory

6.0MiB live, 47.9MiB allocated

Counts

23 → 480

Calls

Call 1

Inputs
#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.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 (cos.f64 x) #s(literal 1/2 binary64)))) (patch (.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 (cos.f64 x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))) (patch #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<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))) (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))) (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))) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (cos.f64 x)) (patch (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 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 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (cos x)) (taylor 0 eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))) (taylor 0 eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor 0 eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor 0 eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (* (pow eps 2) (cos x))) (taylor inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x)))) (taylor inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2)))))) (taylor inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2)))))) (taylor inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (* (pow eps 2) (cos x))) (taylor -inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x)))) (taylor -inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/4 (sin x))) eps)) (* -1/12 (cos x)))) (taylor -inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/4 (sin x))) eps)) (* -1/12 (cos x)))) (taylor -inf eps) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/12 (pow eps 2))) (taylor 0 x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (+ (* -1/4 (* eps x)) (* -1/12 (pow eps 2)))) (taylor 0 x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (+ (* -1/12 (pow eps 2)) (* x (+ (* -1/4 eps) (* x (- (* 1/24 (pow eps 2)) 1/4)))))) (taylor 0 x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (+ (* -1/12 (pow eps 2)) (* x (+ (* -1/4 eps) (* x (- (+ (* 1/24 (* eps x)) (* 1/24 (pow eps 2))) 1/4)))))) (taylor 0 x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor -inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor -inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor -inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))) (taylor -inf x) (#s(alt (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 (cos.f64 x) #s(literal 1/2 binary64))) (patch (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 (cos.f64 x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1/12 (cos x)) (taylor inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (patch (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (sin x)) (taylor 0 eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (* eps (cos x))) (taylor inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x)))) (taylor inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x)))) (taylor inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x)))) (taylor inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/12 (* eps (cos x))) (taylor -inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps))))) (taylor -inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps))))) (taylor -inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps))))) (taylor -inf eps) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/12 eps) (taylor 0 x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 x) (* -1/12 eps)) (taylor 0 x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/12 eps) (* x (- (* 1/24 (* eps x)) 1/4))) (taylor 0 x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/12 eps) (* x (- (* x (+ (* 1/24 eps) (* 1/24 x))) 1/4))) (taylor 0 x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (patch (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	(+ (* (* x -1/2) (+ eps x)) 1)
1.0ms	x	@	-inf	(+ (* eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2))
1.0ms	x	@	inf	(+ (* eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2))
0.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x 1/24)) -1/2)) 1)
0.0ms	eps	@	0	(+ (* eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2))

simplify269.0ms (2.1%)

Memory

-8.6MiB live, 342.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16 006×	`lower-fma.f64`
16 006×	`lower-fma.f32`
6 038×	`lower-*.f64`
6 038×	`lower-*.f32`
4 692×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	389	5060
1	1206	4944
2	3397	4865
0	8391	4479

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 476

Calls

Call 1

Inputs
(* 1/2 (cos x))
(+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(* -1/12 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x))))
(* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2))))))
(* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2))))))
(* -1/12 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/4 (sin x))) eps)) (* -1/12 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/4 (sin x))) eps)) (* -1/12 (cos x))))
(+ 1/2 (* -1/12 (pow eps 2)))
(+ 1/2 (+ (* -1/4 (* eps x)) (* -1/12 (pow eps 2))))
(+ 1/2 (+ (* -1/12 (pow eps 2)) (* x (+ (* -1/4 eps) (* x (- (* 1/24 (pow eps 2)) 1/4))))))
(+ 1/2 (+ (* -1/12 (pow eps 2)) (* x (+ (* -1/4 eps) (* x (- (+ (* 1/24 (* eps x)) (* 1/24 (pow eps 2))) 1/4))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 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)))
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(+ (* 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 (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* -1/12 (* (pow eps 3) (cos x)))
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(* (pow eps 3) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2))))))
(* (pow eps 3) (+ (* -1/4 (/ (sin x) eps)) (+ (* -1/12 (cos x)) (* 1/2 (/ (cos x) (pow eps 2))))))
(* -1/12 (* (pow eps 3) (cos x)))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/4 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/12 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/4 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/12 (cos x)))))
(* eps (+ 1/2 (* -1/12 (pow eps 2))))
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(+ (* eps (+ 1/2 (* -1/12 (pow eps 2)))) (* x (+ (* -1/4 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/4))))))
(+ (* eps (+ 1/2 (* -1/12 (pow eps 2)))) (* x (+ (* -1/4 (pow eps 2)) (* x (+ (* 1/24 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/4)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x)))))))
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(- (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))
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(* 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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
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(* -1/2 (* eps (sin x)))
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(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
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(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
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(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(sin eps)
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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(- (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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
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(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
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(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
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(+ (cos x) (* -1/2 (* eps (sin x))))
1
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(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
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(+ 1 (* -1/2 (pow x 2)))
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(* -1/2 (* eps x))
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(* -1/2 (* eps x))
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(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (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))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
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(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
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(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
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(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
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(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 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))
-1/12
(- (* 1/24 (pow x 2)) 1/12)
(- (* (pow x 2) (+ 1/24 (* -1/288 (pow x 2)))) 1/12)
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/8640 (pow x 2)) 1/288)))) 1/12)
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/12 (cos x))
(* -1/4 (sin x))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(* -1/12 (* eps (cos x)))
(* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x))))
(* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x))))
(* eps (+ (* -1/4 (/ (sin x) eps)) (* -1/12 (cos x))))
(* -1/12 (* eps (cos x)))
(* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/12 (cos x)) (* 1/4 (/ (sin x) eps)))))
(* -1/12 eps)
(+ (* -1/4 x) (* -1/12 eps))
(+ (* -1/12 eps) (* x (- (* 1/24 (* eps x)) 1/4)))
(+ (* -1/12 eps) (* x (- (* x (+ (* 1/24 eps) (* 1/24 x))) 1/4)))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(+ (* -1/4 (sin x)) (* -1/12 (* eps (cos x))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)

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

rewrite275.0ms (2.1%)

Memory

-10.3MiB live, 423.3MiB allocated

Rules

4 672×	`lower-*.f32`
4 648×	`lower-*.f64`
4 110×	`lower-fma.f32`
4 098×	`lower-fma.f64`
3 900×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	364
0	85	360
1	316	360
2	2871	360
0	8645	352

Stop Event

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

Counts

23 → 428

Calls

Call 1

Inputs
(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 (cos.f64 x) #s(literal 1/2 binary64)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64)))))
(.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 (cos.f64 x) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 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))) (cos.f64 x))))
(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) #s(literal -1/12 binary64))
(fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))

Outputs
(+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(+.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps eps)) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(+.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps eps))) (.f64 (sin.f64 x) (*.f64 #s(literal -1/4 binary64) eps)))
(-.f64 (/.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)) (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps)) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps eps) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps)) eps (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (.f64 eps (cos.f64 x)) (.f64 #s(literal -1/12 binary64) eps) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (.f64 eps (.f64 eps (cos.f64 x))) #s(literal -1/12 binary64) (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #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)))) #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)))) (neg.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)))) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/4 binary64)) (pow.f64 (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/4 binary64)))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))))
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(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64)) (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64))) (-.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 (cos.f64 x) (*.f64 #s(literal -1/12 binary64) eps))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (sin.f64 x)))) (.f64 (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (sin.f64 x))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64)))) (.f64 (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (sin.f64 x))) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 #s(literal 1/4 binary64) (sin.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/64 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps))) (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (sin.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64)) (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)))) (neg.f64 (-.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 (cos.f64 x) (*.f64 #s(literal -1/12 binary64) eps)))))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps))) (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/64 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (sin.f64 x))) (-.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64)))) #s(literal -1 binary64))
(.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/64 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/12 binary64) eps))) (.f64 (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)))))
(.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/144 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 #s(literal 1/4 binary64) (sin.f64 x)))))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)

eval106.0ms (0.8%)

Memory: 24.2MiB live, 214.7MiB allocated
Compiler: Compiled 21 258 to 1 621 computations (92.4% saved)

prune156.0ms (1.2%)

Memory

-5.5MiB live, 284.4MiB allocated

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	914	4	918
Fresh	1	5	6
Picked	1	4	5
Done	0	2	2
Total	916	15	931

Accuracy

100.0%

Counts

931 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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))
	99.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	55.1%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
	55.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	99.8%	#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))) (cos.f64 x))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
▶	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 443 to 225 computations (49.2% saved)

simplify236.0ms (1.8%)

Memory

-0.9MiB live, 315.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
cost-diff	320	(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64))
cost-diff	960	(-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
cost-diff	0	(.f64 eps (.f64 x x))
cost-diff	0	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
cost-diff	0	#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
cost-diff	0	#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #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 #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

16 852×	`lower-fma.f32`
16 836×	`lower-fma.f64`
4 484×	`lower-*.f32`
4 448×	`lower-*.f64`
2 548×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	718
0	103	662
1	213	662
2	673	636
3	2533	622
4	3500	622
5	6065	622
0	8246	597

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 #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 #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 #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#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 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
x
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(.f64 eps (.f64 x x))
eps
(*.f64 x x)
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#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))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal -1/8 binary64)
(.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 eps x)
(*.f64 (+.f64 eps x) (+.f64 eps x))
#s(literal 1 binary64)
(-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64))
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(.f64 (+.f64 eps x) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))

Outputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #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 #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 #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 #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#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 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
x
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(.f64 eps (.f64 x x))
eps
(*.f64 x x)
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#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))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 x (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (+.f64 eps x)))) #s(literal 1 binary64)) (fma.f64 x (.f64 (+.f64 eps x) (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 x (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (+.f64 eps x)))) #s(literal 1 binary64)) (fma.f64 x (.f64 (+.f64 eps x) (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 x (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (+.f64 eps x)))) #s(literal 1 binary64)) (fma.f64 x (.f64 (+.f64 eps x) (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(/.f64 (fma.f64 x (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (+.f64 eps x)))) #s(literal 1 binary64)) (fma.f64 x (.f64 (+.f64 eps x) (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64))
(fma.f64 x (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (*.f64 #s(literal -1/8 binary64) (+.f64 eps x)))) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64))
(.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal -1/8 binary64)
(.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))
(+.f64 eps x)
(*.f64 (+.f64 eps x) (+.f64 eps x))
#s(literal 1 binary64)
(-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
(fma.f64 x (.f64 (+.f64 eps x) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64))
(fma.f64 x (.f64 (+.f64 eps x) (.f64 (*.f64 x (+.f64 eps x)) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(.f64 (+.f64 eps x) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
(.f64 x (.f64 (+.f64 eps x) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
(.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))

localize279.0ms (2.2%)

Memory

29.9MiB live, 303.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))
accuracy	0.1328125	(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
accuracy	0.24904252930532605	(*.f64 (+.f64 eps x) (+.f64 eps x))
accuracy	0.5725825466978471	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))
accuracy	0.00390625	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
accuracy	0.00390625	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
accuracy	0.14669107811679954	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
accuracy	0.36587378520411473	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.06640625	(.f64 eps (.f64 x x))
accuracy	0.14669107811679954	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
accuracy	0.31640625	(*.f64 x #s(literal 1/24 binary64))
accuracy	0.47108723661363716	#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
accuracy	0.0078125	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
accuracy	0.012382519536884034	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
accuracy	0.5725825466978471	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
accuracy	62.17801905927488	#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
accuracy	0	(*.f64 eps #s(literal 1/2 binary64))
accuracy	0.006191259768442017	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.0078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.03602182469244065	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

90.0ms	168×	0	valid
67.0ms	88×	1	valid

Compiler

Compiled 422 to 61 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-mult: 69.0ms (54.6% of total)

ival-add: 20.0ms (15.8% of total)

adjust: 10.0ms (7.9% of total)

const: 9.0ms (7.1% of total)

ival-sin: 8.0ms (6.3% of total)

ival-cos: 4.0ms (3.2% of total)

ival-sub: 3.0ms (2.4% of total)

ival-div: 2.0ms (1.6% of total)

exact: 1.0ms (0.8% of total)

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

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

series55.0ms (0.4%)

Memory

-24.3MiB live, 56.9MiB allocated

Counts

28 → 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 #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 #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 #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 #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 #s(literal 1/2 binary64))) (patch #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (patch #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx ( eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) (patch #s(approx ( eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps) (patch (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 x x)) (patch (.f64 eps (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) (patch (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))) (patch (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))) #<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 #s(literal 1/2 binary64)) (patch (.f64 eps #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/24 binary64)) (patch (.f64 x #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))) (patch #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps 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>) () ())) ())
#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 (* 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 (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (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 (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (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 (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (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 (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)) #<representation binary64>) () ())) ())
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#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (+.f64 eps x)) (patch (.f64 (+.f64 eps x) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps x)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/2 eps) (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/2 eps) (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/2 eps) (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) (taylor 0 eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) (taylor 0 eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) (taylor 0 eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps x)) (taylor inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps x)) (taylor -inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3)) (taylor 0 eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3)) (taylor 0 eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3)) (taylor 0 eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) (taylor inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) (taylor inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3)))))))) (taylor inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1))) (taylor -inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) (taylor -inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1))) (taylor -inf eps) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3)) (taylor 0 x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) (taylor 0 x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3)) (taylor 0 x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3)))))))) (taylor inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (patch (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #<representation binary64>) () ())) ())

Calls

150 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	0	(* eps (* x x))
2.0ms	eps	@	0	(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
0.0ms	x	@	inf	(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
0.0ms	eps	@	-inf	(- (+ (* (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x)))
0.0ms	eps	@	0	(- (+ (* (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x)))

simplify264.0ms (2.1%)

Memory

8.6MiB live, 354.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 352×	`lower-fma.f64`
10 352×	`lower-fma.f32`
7 038×	`lower-*.f64`
7 038×	`lower-*.f32`
3 588×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	6375
1	2074	6150
2	6080	6126
0	8938	5658

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)))
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(* 1/2 eps)
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(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))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(- (sin (+ eps x)) (sin x))
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eps
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
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(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
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(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
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1
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(+ (cos x) (* -1/2 (* eps (sin x))))
1
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(* -1/2 (pow x 2))
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(+ 1 (* -1/2 (pow x 2)))
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(sin eps)
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(- (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))
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(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
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(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
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(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
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(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
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(* eps (pow x 2))
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(* eps (pow x 2))
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(* eps (pow x 2))
(* eps (pow x 2))
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(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
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(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(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))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(- (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))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
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(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
1
(+ 1 (* 1/2 (* eps x)))
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(+ 1 (* x (- (* x (+ 1/2 (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps x))))) (* -1/2 eps))))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/2 (/ eps x))))
(* (pow x 4) (+ 1/4 (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 (/ eps x)) (/ 1/2 (pow x 2))))))
(* (pow x 4) (+ 1/4 (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1/2 (pow x 2)))))))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/2 (/ eps x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/4 (pow eps 2))) x)) (* -1/2 eps)) x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* 1/4 (pow eps 2)) (* 1/2 (/ eps x)))) x)) (* -1/2 eps)) x))))
(- (+ 1 (* 1/4 (pow x 4))) (* -1/2 (pow x 2)))
(- (+ 1 (+ (* 1/4 (pow x 4)) (* eps (- (* 1/2 (pow x 3)) (* -1/2 x))))) (* -1/2 (pow x 2)))
(- (+ 1 (+ (* 1/4 (pow x 4)) (* eps (- (+ (* 1/4 (* eps (pow x 2))) (* 1/2 (pow x 3))) (* -1/2 x))))) (* -1/2 (pow x 2)))
(- (+ 1 (+ (* 1/4 (pow x 4)) (* eps (- (+ (* 1/4 (* eps (pow x 2))) (* 1/2 (pow x 3))) (* -1/2 x))))) (* -1/2 (pow x 2)))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (* 1/2 (/ (pow x 3) eps))) (* -1/2 (/ x eps))))
(* (pow eps 2) (- (+ (* 1/4 (/ (pow x 4) (pow eps 2))) (+ (* 1/4 (pow x 2)) (+ (* 1/2 (/ (pow x 3) eps)) (/ 1 (pow eps 2))))) (+ (* -1/2 (/ x eps)) (* -1/2 (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (- (+ (* 1/4 (/ (pow x 4) (pow eps 2))) (+ (* 1/4 (pow x 2)) (+ (* 1/2 (/ (pow x 3) eps)) (/ 1 (pow eps 2))))) (+ (* -1/2 (/ x eps)) (* -1/2 (/ (pow x 2) (pow eps 2))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/2 (pow x 3)) (* 1/2 x)) eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ 1 (* 1/4 (pow x 4))) (* -1/2 (pow x 2))) eps)) (* -1/2 (pow x 3))) (* 1/2 x)) eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ 1 (* 1/4 (pow x 4))) (* -1/2 (pow x 2))) eps)) (* -1/2 (pow x 3))) (* 1/2 x)) eps)) (* 1/4 (pow x 2))))
1
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(+ 1 (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps x)))))
(+ 1 (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* x (+ (* 1/4 x) (* 1/2 eps))))))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/2 (/ eps x))))
(* (pow x 4) (+ 1/4 (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 (/ eps x)))))
(* (pow x 4) (+ 1/4 (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 (/ eps x)) (/ 1 (pow x 4))))))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* 1/2 (/ eps x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ 1 (pow x 2))) x)) (* -1/2 eps)) x))))
(+ 1 (* 1/4 (pow x 4)))
(+ 1 (+ (* 1/4 (pow x 4)) (* 1/2 (* eps (pow x 3)))))
(+ 1 (+ (* 1/4 (pow x 4)) (* eps (+ (* 1/4 (* eps (pow x 2))) (* 1/2 (pow x 3))))))
(+ 1 (+ (* 1/4 (pow x 4)) (* eps (+ (* 1/4 (* eps (pow x 2))) (* 1/2 (pow x 3))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/4 (pow x 2)) (* 1/2 (/ (pow x 3) eps))))
(* (pow eps 2) (+ (* 1/4 (/ (pow x 4) (pow eps 2))) (+ (* 1/4 (pow x 2)) (+ (* 1/2 (/ (pow x 3) eps)) (/ 1 (pow eps 2))))))
(* (pow eps 2) (+ (* 1/4 (/ (pow x 4) (pow eps 2))) (+ (* 1/4 (pow x 2)) (+ (* 1/2 (/ (pow x 3) eps)) (/ 1 (pow eps 2))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/4 (pow x 2)) (* 1/2 (/ (pow x 3) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/4 (pow x 4))) eps)) (* -1/2 (pow x 3))) eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/4 (pow x 4))) eps)) (* -1/2 (pow x 3))) eps)) (* 1/4 (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))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos (* 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)
(* 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)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(pow x 3)
(+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3))
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3))
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3))
(pow eps 3)
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1)))
(pow eps 3)
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3))
(pow x 3)
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x))))
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))))
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3))))))))
(pow x 3)
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1)))

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

rewrite337.0ms (2.6%)

Memory

2.7MiB live, 410.7MiB allocated

Rules

6 550×	`lower-*.f32`
6 514×	`lower-*.f64`
5 068×	`lower-fma.f32`
5 052×	`lower-fma.f64`
3 454×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	564
0	103	526
1	400	501
2	3571	432
0	9707	416

Stop Event

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

Counts

28 → 529

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 #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 #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 #s(literal 1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(.f64 eps (.f64 x x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))
(*.f64 (+.f64 eps x) (+.f64 eps x))
(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
(.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps 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 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 eps (.f64 eps eps)))) (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 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 eps (.f64 eps eps))) #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 (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 #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 #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 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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)))) #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (.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(approx (sin ( (+ eps 0) 1/2)) (.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))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(+.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #s(literal 0 binary64)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #s(literal 0 binary64)))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) eps (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #s(literal 0 binary64)))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) eps (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) #s(literal 0 binary64) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) eps)
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))) eps)
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps)))
#s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps))
(+.f64 eps (.f64 eps (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(+.f64 eps (+.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))))
(+.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps))
(+.f64 (fma.f64 eps (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) eps) #s(literal 0 binary64))
(+.f64 (.f64 eps (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 eps (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (fma.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))) eps))
(+.f64 (+.f64 eps (.f64 (.f64 x x) (.f64 eps (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(+.f64 (fma.f64 eps (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) #s(literal 0 binary64)) eps)
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(exp.f64 (*.f64 (log.f64 (+.f64 x eps)) #s(literal 3 binary64)))
(+.f64 (.f64 (+.f64 x eps) (.f64 eps (+.f64 x eps))) (.f64 (+.f64 x eps) (.f64 x (+.f64 x eps))))
(+.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) eps))
(+.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) eps) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) x))
(+.f64 (.f64 (.f64 eps (+.f64 x eps)) (+.f64 x eps)) (.f64 (.f64 x (+.f64 x eps)) (+.f64 x eps)))
(+.f64 (.f64 x (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 eps (.f64 (+.f64 x eps) (+.f64 x eps))))
(+.f64 (.f64 eps (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 (+.f64 x eps) (+.f64 x eps))))
(fma.f64 x (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 eps (*.f64 (+.f64 x eps) (+.f64 x eps))))
(fma.f64 eps (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (*.f64 (+.f64 x eps) (+.f64 x eps))))
(fma.f64 (+.f64 x eps) (.f64 eps (+.f64 x eps)) (.f64 (+.f64 x eps) (*.f64 x (+.f64 x eps))))
(fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) x (.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)) eps))
(fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) eps (.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)) x))
(fma.f64 (.f64 eps (+.f64 x eps)) (+.f64 x eps) (.f64 (*.f64 x (+.f64 x eps)) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal 3 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.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 (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))))
(/.f64 (.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 (-.f64 x eps) (.f64 (-.f64 x eps) (-.f64 x eps)))) (.f64 (-.f64 x eps) (*.f64 (-.f64 x eps) (-.f64 x eps))))
(/.f64 (.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 (-.f64 eps x) (.f64 (-.f64 eps x) (-.f64 eps x)))) (.f64 (-.f64 eps x) (*.f64 (-.f64 eps x) (-.f64 eps x))))
(/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 x eps) (+.f64 x eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 x eps) (+.f64 x eps))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (+.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (*.f64 (+.f64 x eps) (+.f64 x eps))) (-.f64 eps x))
(/.f64 (pow.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (-.f64 eps x)) #s(literal 3 binary64)))
(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
(pow.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (+.f64 x eps) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 x eps))) #s(literal 3 binary64))
(.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))
(.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps))
(.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64)))
(.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) #s(literal 3 binary64)))
(.f64 (.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 (-.f64 x eps) (.f64 (-.f64 x eps) (-.f64 x eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) #s(literal 3 binary64)))
(.f64 (.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 (-.f64 eps x) (.f64 (-.f64 eps x) (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps x)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (+.f64 x eps) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x eps) #s(literal 3/2 binary64)))

eval159.0ms (1.2%)

Memory: 1.0MiB live, 226.1MiB allocated
Compiler: Compiled 49 897 to 3 074 computations (93.8% saved)

prune181.0ms (1.4%)

Memory

30.1MiB live, 234.1MiB allocated

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	1 176	2	1 178
Fresh	1	3	4
Picked	2	3	5
Done	0	6	6
Total	1 179	14	1 193

Accuracy

100.0%

Counts

1 193 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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))
	99.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	55.1%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	99.8%	#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))) (cos.f64 x))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
✓	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 600 to 228 computations (62% saved)

regimes39.0ms (0.3%)

Memory

-21.4MiB live, 18.8MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 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))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(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 (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))))
(.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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.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 (cos.f64 x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

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

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)

regimes20.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 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))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(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 (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))))
(.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
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))

Calls

3 calls:

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

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)

regimes33.0ms (0.3%)

Memory

-15.9MiB live, 22.8MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 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))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(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 (sin.f64 (+.f64 x eps)) (sin.f64 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))

Calls

3 calls:

21.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	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)

regimes19.0ms (0.1%)

Memory

-10.5MiB live, 27.1MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 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))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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))

Outputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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:

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

regimes15.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 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))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))

Outputs
#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))) (cos.f64 x))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-16.9MiB live, 21.4MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 eps #s(approx (+ ( eps (+ (* eps (* (cos x) -1/12)) (* (sin x) -1/4))) (* (cos x) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) #s(approx (- (+ ( (* x -1/2) (* (+ eps x) (* (* x -1/2) (+ eps x)))) 1) (* (* x -1/2) (+ eps x))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal 1 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 eps x) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #s(literal 1 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-24.9MiB live, 14.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	eps
3.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

-25.9MiB live, 10.4MiB allocated

Accuracy

Total -59.9b remaining (-6088.8%)

Threshold costs -59.9b (-6088.8%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

6.0ms	x
2.0ms	eps
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Algorithm

1×	egg-herbie

Rules

48×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	264
1	118	264

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.0s (8.1%)

Memory

19.2MiB live, 808.6MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
13 684×	`lower-fma.f64`
13 684×	`lower-fma.f32`
10 352×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	6375
1	2074	6150
2	6080	6126
0	8938	5658
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	359	3321
1	1096	3209
2	2836	3169
3	6540	3169
0	8160	2921
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Compiler

Compiled 330 to 182 computations (44.8% saved)

preprocess139.0ms (1.1%)

Memory: -31.1MiB live, 225.0MiB allocated
Compiler: Compiled 400 to 188 computations (53% 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%)

analyze55.0ms (0.4%)

sample6.1s (47.6%)

explain90.0ms (0.7%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.1%)

localize25.0ms (0.2%)

series4.0ms (0%)

simplify243.0ms (1.9%)

rewrite328.0ms (2.6%)

eval131.0ms (1%)

prune62.0ms (0.5%)

simplify259.0ms (2%)

localize127.0ms (1%)

series51.0ms (0.4%)

simplify357.0ms (2.8%)

rewrite484.0ms (3.8%)

eval154.0ms (1.2%)

prune181.0ms (1.4%)

simplify213.0ms (1.7%)

localize175.0ms (1.4%)

series35.0ms (0.3%)

simplify269.0ms (2.1%)

rewrite275.0ms (2.1%)

eval106.0ms (0.8%)

prune156.0ms (1.2%)

simplify236.0ms (1.8%)

localize279.0ms (2.2%)

series55.0ms (0.4%)

simplify264.0ms (2.1%)

rewrite337.0ms (2.6%)

eval159.0ms (1.2%)

prune181.0ms (1.4%)

regimes39.0ms (0.3%)

regimes20.0ms (0.2%)

regimes33.0ms (0.3%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

regimes9.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.0s (8.1%)

preprocess139.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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