Metrics for 2sin (example 3.3)

analyze41.0ms (0.3%)

Memory

-14.2MiB live, 63.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.7s (38.6%)

Memory

-124.1MiB live, 7 456.3MiB allocated

Samples

2.9s	26 155×	0	invalid
893.0ms	5 568×	0	valid
472.0ms	2 688×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

const: 635.0ms (21.6% of total)

ival-sin: 634.0ms (21.5% of total)

ival-<=: 319.0ms (10.8% of total)

ival-mult: 272.0ms (9.2% of total)

ival-add: 236.0ms (8% of total)

ival-fabs: 235.0ms (8% of total)

ival-sub: 204.0ms (6.9% of total)

ival-<: 183.0ms (6.2% of total)

ival-and: 100.0ms (3.4% of total)

adjust: 70.0ms (2.4% of total)

exact: 46.0ms (1.6% of total)

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

Bogosity

preprocess27.0ms (0.2%)

Memory

6.2MiB live, 45.4MiB 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))

explain96.0ms (0.7%)

Memory

28.7MiB live, 107.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	3	(1.0842137292829784e-97 7.629361084465591e-100)	9	(-1.0729840744805937e-269 1.1497784130418687e-271)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	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	218	12
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	216	9
-	3	28

Precision

0.9863013698630136

Recall

0.96

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	9	0
-	3	3	25

Precision?

0.974025974025974

Recall?

1.0

Freqs

test

number	freq
0	37
1	218
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	158×	1	valid
17.0ms	352×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sin: 10.0ms (49.6% of total)

adjust: 3.0ms (14.9% of total)

ival-add: 3.0ms (14.9% of total)

ival-sub: 3.0ms (14.9% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

-33.8MiB live, 6.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize24.0ms (0.2%)

Memory

36.7MiB live, 36.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	64.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

8.0ms	176×	0	valid
8.0ms	79×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sin: 5.0ms (52% of total)

adjust: 2.0ms (20.8% of total)

ival-add: 2.0ms (20.8% of total)

ival-sub: 1.0ms (10.4% of total)

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

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

series6.0ms (0%)

Memory

-30.1MiB live, 7.8MiB 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	(+ x eps)
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))

simplify374.0ms (2.5%)

Memory

-1.7MiB live, 476.7MiB 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 (2.2%)

Memory

36.6MiB live, 355.8MiB allocated

Algorithm

1×	batch-egg-rewrite

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 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x 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 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x 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))

eval39.0ms (0.3%)

Memory: -32.0MiB live, 84.4MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune43.0ms (0.3%)

Memory

28.5MiB live, 105.8MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

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

Accuracy

100.0%

Counts

292 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	64.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	64.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
▶	63.7%	(-.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))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 265 to 164 computations (38.1% saved)

simplify413.0ms (2.8%)

Memory

-23.4MiB live, 392.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

9 858×	`lower-fma.f32`
9 848×	`lower-fma.f64`
5 936×	`lower-*.f32`
5 914×	`lower-*.f64`
1 866×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	267
0	71	249
1	119	249
2	259	249
3	532	245
4	857	245
5	1202	245
6	1545	245
7	1641	245
8	1729	245
9	1764	245
10	1936	245
11	3291	245
12	3750	245
13	4484	245
14	5054	245
15	5234	245
16	5499	245
17	6035	245
18	6731	245
19	7135	245
20	7276	245
0	8050	238

Stop Event

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

Calls

Call 1

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

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

localize135.0ms (0.9%)

Memory

14.2MiB live, 249.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
✓	accuracy	100.0%	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
✓	accuracy	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	accuracy	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	98.9%	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	accuracy	64.3%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
✓	accuracy	100.0%	(.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	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.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))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

48.0ms	176×	0	valid
37.0ms	79×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 233 to 39 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 28.0ms (45% of total)

ival-add: 10.0ms (16.1% of total)

ival-sin: 8.0ms (12.9% of total)

adjust: 6.0ms (9.6% of total)

ival-cos: 5.0ms (8% of total)

const: 4.0ms (6.4% of total)

ival-sub: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

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

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

series50.0ms (0.3%)

Memory

10.5MiB live, 47.5MiB allocated

Counts

22 → 432

Calls

Call 1

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

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

Calls

108 calls:

Time	Variable		Point	Expression
16.0ms	x	@	-inf	(sin x)
2.0ms	eps	@	0	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))

simplify479.0ms (3.2%)

Memory

-4.1MiB live, 517.5MiB allocated

Algorithm

1×	egg-herbie

Rules

17 630×	`lower-fma.f64`
17 630×	`lower-fma.f32`
6 184×	`lower-*.f64`
6 184×	`lower-*.f32`
4 734×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	405	4067
1	1275	3889
2	3541	3851
0	8094	3528

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 408

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* 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 (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(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))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1
(+ 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)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)

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

rewrite618.0ms (4.2%)

Memory

-5.2MiB live, 307.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 204×	`lower-fma.f32`
6 194×	`lower-fma.f64`
4 424×	`lower-*.f32`
4 402×	`lower-*.f64`
3 988×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	205
0	71	191
1	233	191
2	1924	191
0	8414	191

Stop Event

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

Counts

22 → 657

Calls

Call 1

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

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

eval228.0ms (1.5%)

Memory: 1.7MiB live, 198.9MiB allocated
Compiler: Compiled 29 049 to 2 603 computations (91% saved)

prune160.0ms (1.1%)

Memory

-15.5MiB live, 302.6MiB allocated

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	1 077	15	1 092
Fresh	2	2	4
Picked	4	1	5
Done	1	0	1
Total	1 084	18	1 102

Accuracy

100.0%

Counts

1 102 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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)))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
▶	98.7%	#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)))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 675 to 376 computations (44.3% saved)

simplify333.0ms (2.3%)

Memory

32.9MiB live, 512.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
✓	cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
✓	cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
✓	cost-diff	128	(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x))))
✓	cost-diff	384	(fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #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 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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))))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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)))))) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

13 432×	`lower-fma.f32`
13 420×	`lower-fma.f64`
3 864×	`lower-*.f32`
3 830×	`lower-*.f64`
2 852×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	600
0	104	578
1	191	546
2	501	546
3	1567	546
4	3408	538
5	3898	538
6	4447	538
7	6299	538
0	8017	513

Stop Event

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

Calls

Call 1

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

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

localize210.0ms (1.4%)

Memory

-15.0MiB live, 375.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
✓	accuracy	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))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	97.9%	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
✓	accuracy	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
✓	accuracy	99.8%	(*.f64 eps (+.f64 eps x))
✓	accuracy	99.7%	(.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))
✓	accuracy	98.9%	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))
✓	accuracy	100.0%	(.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))))
✓	accuracy	100.0%	(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
✓	accuracy	99.5%	#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	98.9%	#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	100.0%	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
✓	accuracy	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
✓	accuracy	97.7%	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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))))))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(-.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)))))

Samples

64.0ms	177×	0	valid
52.0ms	77×	1	valid
3.0ms	2×	5	exit

Compiler

Compiled 437 to 54 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 37.0ms (41.5% of total)

ival-add: 15.0ms (16.8% of total)

adjust: 9.0ms (10.1% of total)

ival-sin: 9.0ms (10.1% of total)

ival-cos: 8.0ms (9% of total)

const: 7.0ms (7.9% of total)

ival-sub: 3.0ms (3.4% of total)

exact: 1.0ms (1.1% of total)

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

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

series57.0ms (0.4%)

Memory

-2.6MiB live, 55.2MiB allocated

Counts

26 → 564

Calls

Call 1

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

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

Calls

141 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)

simplify336.0ms (2.3%)

Memory

-8.6MiB live, 417.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 246×	`lower-fma.f64`
12 246×	`lower-fma.f32`
7 646×	`lower-*.f64`
7 646×	`lower-*.f32`
2 358×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	520	6787
1	1674	6629
2	5200	6615
0	8417	6144

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 538

Calls

Call 1

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

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

rewrite465.0ms (3.1%)

Memory

43.3MiB live, 279.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 076×	`lower-*.f32`
7 042×	`lower-*.f64`
4 120×	`lower-fma.f32`
4 108×	`lower-fma.f64`
3 588×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	479
0	104	457
1	368	414
2	3353	414
0	9937	397

Stop Event

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

Counts

26 → 407

Calls

Call 1

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

Outputs
x
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(pow.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 2 binary64) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) x)
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal 2 binary64))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (/.f64 eps (*.f64 eps eps)) 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 (.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 (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 (-.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)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.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 2 binary64) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.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)))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)))))
(+.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)))))
(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))))
(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))))
(/.f64 (.f64 (.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
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(+.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) x) (.f64 (.f64 eps #s(literal 1/12 binary64)) eps))
(+.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) eps) (.f64 (.f64 eps #s(literal 1/12 binary64)) x))
(+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(+.f64 (.f64 x (.f64 eps #s(literal 1/12 binary64))) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))
(+.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x (.f64 eps #s(literal 1/12 binary64))))
(fma.f64 x (.f64 eps #s(literal 1/12 binary64)) (.f64 eps (*.f64 eps #s(literal 1/12 binary64))))
(fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (.f64 x (*.f64 eps #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x eps)))
(fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (.f64 (*.f64 x eps) #s(literal 1/12 binary64)))
(fma.f64 (.f64 eps #s(literal 1/12 binary64)) x (.f64 (*.f64 eps #s(literal 1/12 binary64)) eps))
(fma.f64 (.f64 eps #s(literal 1/12 binary64)) eps (.f64 (*.f64 eps #s(literal 1/12 binary64)) x))
(/.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 (.f64 eps #s(literal 1/12 binary64)) (*.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)))
(.f64 (+.f64 x eps) (.f64 eps #s(literal 1/12 binary64)))
(.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 x eps)))
(.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64))
(.f64 (.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))
(.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps)
(+.f64 (.f64 eps (+.f64 x eps)) (.f64 (+.f64 x eps) #s(literal 0 binary64)))
(+.f64 (.f64 eps (+.f64 x eps)) (.f64 #s(literal 0 binary64) (+.f64 x eps)))
(+.f64 (.f64 eps eps) (.f64 x eps))
(+.f64 (.f64 x eps) (.f64 eps eps))
(+.f64 (.f64 (+.f64 x eps) #s(literal 0 binary64)) (.f64 eps (+.f64 x eps)))
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 x eps)) (.f64 eps (+.f64 x eps)))
(fma.f64 x eps (*.f64 eps eps))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x eps))
(fma.f64 eps (+.f64 x eps) (*.f64 (+.f64 x eps) #s(literal 0 binary64)))
(fma.f64 eps (+.f64 x eps) (*.f64 #s(literal 0 binary64) (+.f64 x eps)))
(fma.f64 #s(literal 0 binary64) (+.f64 x eps) (*.f64 eps (+.f64 x eps)))
(fma.f64 (+.f64 x eps) eps (*.f64 (+.f64 x eps) #s(literal 0 binary64)))
(fma.f64 (+.f64 x eps) eps (*.f64 #s(literal 0 binary64) (+.f64 x eps)))
(fma.f64 (+.f64 x eps) #s(literal 0 binary64) (*.f64 eps (+.f64 x eps)))
(fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 2 binary64)) (*.f64 x eps))
(fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64)) (.f64 x eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 (.f64 eps eps) (-.f64 x eps)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 eps x))) (.f64 (.f64 eps eps) (-.f64 eps x)))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 eps (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 eps (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 eps eps) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 eps (-.f64 x eps)))
(/.f64 (.f64 (.f64 eps eps) (.f64 (+.f64 x eps) (-.f64 eps x))) (.f64 eps (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) eps))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 eps eps)) (.f64 (-.f64 x eps) eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 eps x) (.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (.f64 eps eps)) (.f64 (-.f64 eps x) eps))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 eps (.f64 eps eps)) eps (-.f64 (.f64 (.f64 x x) (.f64 eps eps)) (.f64 (.f64 eps eps) (*.f64 x eps)))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 (.f64 x x) (.f64 eps eps))) (*.f64 eps (-.f64 eps x)))
(/.f64 (.f64 eps (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 eps (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 eps (.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 eps (.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 (+.f64 x eps) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (+.f64 x eps) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 x eps)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (+.f64 x eps)) eps)
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) eps) (-.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) eps) (-.f64 eps x))
(*.f64 eps (+.f64 x eps))
(*.f64 (+.f64 x eps) eps)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64)) (.f64 eps eps))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)

eval170.0ms (1.1%)

Memory: -21.4MiB live, 130.3MiB allocated
Compiler: Compiled 25 710 to 2 206 computations (91.4% saved)

prune137.0ms (0.9%)

Memory

13.9MiB live, 137.8MiB allocated

Pruning

20 alts after pruning (16 fresh and 4 done)

	Pruned	Kept	Total
New	948	10	958
Fresh	6	6	12
Picked	2	3	5
Done	0	1	1
Total	956	20	976

Accuracy

100.0%

Counts

976 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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)))) #s(approx ( (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	33.1%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
✓	98.7%	#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)))))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	5.1%	#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)))))))
▶	5.6%	#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 eps #s(literal -1/2 binary64)))))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))

Compiler

Compiled 748 to 420 computations (43.9% saved)

simplify498.0ms (3.4%)

Memory

-27.5MiB live, 339.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
✓	cost-diff	128	(+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
✓	cost-diff	384	(fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
✓	cost-diff	0	(fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #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 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
✓	cost-diff	0	#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #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 eps #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 eps #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 eps #s(literal -1/2 binary64)))))))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

16 324×	`lower-fma.f32`
16 304×	`lower-fma.f64`
3 942×	`lower-*.f32`
3 896×	`lower-*.f64`
3 106×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	801
0	137	773
1	262	737
2	641	737
3	1855	724
4	2554	724
5	2938	724
6	3415	724
7	4689	724
8	7519	724
0	8185	695

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))))
(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)
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))))
(cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(*.f64 eps eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))
#s(literal 1/384 binary64)
#s(literal -1/8 binary64)
#s(literal 1 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))))
(sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.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 eps #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 eps #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 eps #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 eps #s(literal -1/2 binary64)))
x
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
x
(fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64)))
x
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(.f64 (.f64 x x) (fma.f64 eps (*.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(*.f64 x x)
(fma.f64 eps (*.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
(+.f64 x eps)
#s(literal 1/12 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal -1/48 binary64))
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
(.f64 (fma.f64 #s(approx (cos ( eps 1/2)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(approx (cos (* eps 1/2)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 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)
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))
(fma.f64 #s(approx (cos (* eps 1/2)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))))
(.f64 #s(approx (cos ( eps 1/2)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (cos.f64 x))
(cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(cos.f64 x)
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
x
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
#s(approx (cos (* eps 1/2)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))
(*.f64 eps eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))
#s(literal 1/384 binary64)
#s(literal -1/8 binary64)
#s(literal 1 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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))
(sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sin.f64 x)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.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 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 eps (.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 eps #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 eps (.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 eps #s(literal -1/2 binary64)))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
(.f64 x (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
x
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
x
(fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64)))
(fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 (+.f64 eps x) (.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 (+.f64 eps x) (.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 (+.f64 eps x) (.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(fma.f64 (+.f64 eps x) (.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(fma.f64 (+.f64 eps x) (.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))
(fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))
x
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(.f64 (.f64 x x) (fma.f64 eps (*.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 x x) (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)))
(*.f64 x x)
(fma.f64 eps (*.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64))
(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
#s(literal 1/12 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
(*.f64 eps #s(literal -1/48 binary64))
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

localize357.0ms (2.4%)

Memory

35.2MiB live, 423.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/48 binary64))
✓	accuracy	99.8%	(fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
✓	accuracy	99.5%	(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	98.9%	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/12 binary64))
✓	accuracy	98.9%	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64))))))
✓	accuracy	99.5%	#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 eps #s(literal -1/2 binary64)))))))
✓	accuracy	98.9%	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64)))))
✓	accuracy	4.5%	#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	100.0%	#s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))

Samples

95.0ms	77×	1	valid
93.0ms	174×	0	valid
25.0ms	3×	5	exit
1.0ms	1×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 529 to 80 computations (84.9% saved)

Precisions

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

ival-mult: 58.0ms (36.3% of total)

const: 42.0ms (26.3% of total)

ival-add: 24.0ms (15% of total)

adjust: 14.0ms (8.8% of total)

ival-sin: 9.0ms (5.6% of total)

ival-cos: 8.0ms (5% of total)

ival-sub: 3.0ms (1.9% of total)

exact: 1.0ms (0.6% of total)

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

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

series51.0ms (0.3%)

Memory

8.2MiB live, 87.2MiB allocated

Counts

31 → 648

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #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))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) (patch (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #<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 eps #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 eps #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 eps #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 eps #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 eps #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 eps #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) (patch #s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #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 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (patch (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (patch (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (patch (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))) #<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 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))) (patch (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/12 binary64)) (patch (.f64 eps #s(literal 1/12 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #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 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #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 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/12 eps) (* 1/12 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/12 eps) (* 1/12 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/12 (* 1/12 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/12 (* 1/12 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/12 (* 1/12 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor -inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/12 (/ eps x)) 1/12))) (taylor -inf x) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 x) (taylor 0 eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/12 eps) (* 1/12 x)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/12 eps) (* 1/12 x)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/12 eps) (* 1/12 x)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 eps) (taylor inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/12 (* 1/12 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/12 (* 1/12 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/12 (* 1/12 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/12 eps) (taylor -inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/12 (/ x eps)) 1/12))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/12 (/ x eps)) 1/12))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/12 (/ x eps)) 1/12))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) (patch (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/48 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/48 (pow eps 3)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/48 (pow eps 3)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

162 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(+ (* x (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2))) 1)
1.0ms	eps	@	inf	(+ (* x (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2))) 1)
1.0ms	eps	@	-inf	(+ (* x (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2))) 1)
0.0ms	eps	@	inf	(* eps (+ (* eps (* eps -1/48)) 1/2))
0.0ms	eps	@	0	(* eps (+ (* eps (* eps -1/48)) 1/2))

simplify389.0ms (2.6%)

Memory

-16.8MiB live, 699.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 502×	`lower-fma.f64`
12 502×	`lower-fma.f32`
6 958×	`lower-*.f64`
6 958×	`lower-*.f32`
3 298×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	623	7837
1	1989	7560
2	6118	7536
0	8247	6986

Stop Event

1×	iter limit
1×	node limit

Counts

648 → 619

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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eps
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1
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1
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eps
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1
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1
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(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
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(* -1/6 (pow eps 2))
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(+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))))
(* 1/12 (* eps (pow x 3)))
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(* 1/12 (* eps (pow x 3)))
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(+ 1 (* -1/2 (pow x 2)))
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(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* 1/12 (/ (pow x 3) eps)) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (/ (pow x 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (/ (pow x 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/12 (pow x 3)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (+ (* -1/12 (pow x 3)) (* 1/2 x))) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (+ (* -1/12 (pow x 3)) (* 1/2 x))) eps)) (* 1/12 (pow x 2))) 1/6))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(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 x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(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 x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
1
(+ 1 (* -1/8 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(* eps (- (* 1/12 (pow x 2)) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* 1/12 x)
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* 1/12 x)
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(+ (* 1/12 eps) (* 1/12 x))
(* 1/12 eps)
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* 1/12 eps)
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))

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

rewrite316.0ms (2.1%)

Memory

-11.9MiB live, 428.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 722×	`lower-fma.f32`
5 702×	`lower-fma.f64`
4 820×	`lower-*.f32`
4 774×	`lower-*.f64`
2 556×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	639
0	137	611
1	505	591
2	4436	591
0	8132	567

Stop Event

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

Counts

31 → 401

Calls

Call 1

Inputs
(.f64 (.f64 x #s(literal 2 binary64)) #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))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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))))))
#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 eps #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 eps #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 eps #s(literal -1/2 binary64)))))
#s(approx (+ (* (* x -1/2) (+ eps x)) 1) (.f64 x (.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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
#s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(*.f64 eps #s(literal 1/12 binary64))
(fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
(*.f64 eps #s(literal -1/48 binary64))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))

Outputs
x
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(pow.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 2 binary64) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) x)
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal 2 binary64))
eps
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 eps eps) eps)
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (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 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)))))
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)))))
(+.f64 (.f64 (.f64 #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)))))
(fma.f64 (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (pow.f64 (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64)))))))
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(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (.f64 eps (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/96 binary64))) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) (.f64 eps eps)) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))) eps))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64))) (.f64 eps (.f64 eps eps)) (.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps))) (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) eps)
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) eps) (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) eps)

eval407.0ms (2.8%)

Memory: -175.5MiB live, 248.8MiB allocated
Compiler: Compiled 28 623 to 2 205 computations (92.3% saved)

prune193.0ms (1.3%)

Memory

17.8MiB live, 250.6MiB allocated

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	1 025	8	1 033
Fresh	5	6	11
Picked	3	2	5
Done	1	3	4
Total	1 034	19	1 053

Accuracy

100.0%

Counts

1 053 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.6%	(.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))
	33.1%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
✓	98.7%	#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)))))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
	5.1%	#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)))))))
✓	5.6%	#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 eps #s(literal -1/2 binary64)))))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))

Compiler

Compiled 1 135 to 398 computations (64.9% saved)

regimes36.0ms (0.2%)

Memory

-7.8MiB live, 30.6MiB allocated

Counts

43 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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)))) #s(approx ( (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 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)))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #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)))))) #s(literal 2 binary64))

Outputs

(*.f64 (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (*.f64 #s(approx (cos (* eps 1/2)) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))

Calls

3 calls:

13.0ms	x
11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	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)

regimes31.0ms (0.2%)

Memory

27.0MiB live, 27.0MiB allocated

Counts

38 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))

Outputs

(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (*.f64 eps (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))

Calls

3 calls:

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

regimes41.0ms (0.3%)

Memory

0.5MiB live, 40.5MiB allocated

Counts

37 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))

Outputs

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

Calls

3 calls:

20.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

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)

regimes27.0ms (0.2%)

Memory

1.6MiB live, 39.3MiB allocated

Counts

31 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

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

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)

regimes25.0ms (0.2%)

Memory

-2.3MiB live, 35.8MiB allocated

Counts

28 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.2%)

Memory

0.4MiB live, 37.1MiB allocated

Counts

25 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))

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

Calls

3 calls:

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

regimes23.0ms (0.2%)

Memory

-17.1MiB live, 26.0MiB 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) #s(literal 1 binary64)))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps #s(approx ( (+ x eps) 1/12) (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x x) (fma.f64 eps (.f64 (+.f64 x eps) #s(literal 1/12 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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps (+.f64 eps x)))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 eps eps)) #s(literal 1/12 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-13.0MiB live, 26.0MiB allocated

Counts

14 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* x (+ (* x (* eps 1/12)) -1/2)) (* eps -1/2)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

24.3MiB live, 24.3MiB 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #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:

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

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-19.5MiB live, 18.1MiB allocated

Counts

9 → 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (+ (* eps (+ (* x -1/2) (* eps -1/6))) (* (* x x) (+ (* eps (* (+ x eps) 1/12)) -1/2))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))

Outputs

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

Calls

3 calls:

5.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

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)

regimes8.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

12.1MiB live, 12.1MiB 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 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)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-28.2MiB live, 10.8MiB allocated

Accuracy

Total -59.4b remaining (-4172.9%)

Threshold costs -59.4b (-4172.9%)

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 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)))))))

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:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.8%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB allocated

Algorithm

1×	egg-herbie

Rules

68×	`*-commutative_binary64`
10×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	138	435
1	181	435
2	186	435
3	189	435
4	190	435

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) 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 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x)) (.f64 #s(approx (cos ( eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) #s(approx (cos (* eps 1/2)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) #s(approx (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #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 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) #s(approx (+ -1/2 (* 1/12 (* eps (+ eps x)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (+ (* eps -1/6) (* x -1/2))) (+ (* (* x x) (+ -1/2 (* 1/12 (* eps (+ eps x))))) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 (.f64 eps eps) #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))))

soundness1.6s (11%)

Memory

61.2MiB live, 1 141.6MiB allocated

Rules

17 630×	`lower-fma.f64`
17 630×	`lower-fma.f32`
16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
12 502×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	623	7837
1	1989	7560
2	6118	7536
0	8247	6986
0	41	205
0	71	191
1	233	191
2	1924	191
0	8414	191
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	405	4067
1	1275	3889
2	3541	3851
0	8094	3528
0	86	639
0	137	611
1	505	591
2	4436	591
0	8132	567
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	520	6787
1	1674	6629
2	5200	6615
0	8417	6144

Stop Event

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

Compiler

Compiled 690 to 365 computations (47.1% saved)

preprocess171.0ms (1.2%)

Memory: -61.8MiB live, 226.5MiB allocated
Compiler: Compiled 554 to 228 computations (58.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

analyze41.0ms (0.3%)

sample5.7s (38.6%)

preprocess27.0ms (0.2%)

explain96.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize24.0ms (0.2%)

series6.0ms (0%)

simplify374.0ms (2.5%)

rewrite328.0ms (2.2%)

eval39.0ms (0.3%)

prune43.0ms (0.3%)

simplify413.0ms (2.8%)

localize135.0ms (0.9%)

series50.0ms (0.3%)

simplify479.0ms (3.2%)

rewrite618.0ms (4.2%)

eval228.0ms (1.5%)

prune160.0ms (1.1%)

simplify333.0ms (2.3%)

localize210.0ms (1.4%)

series57.0ms (0.4%)

simplify336.0ms (2.3%)

rewrite465.0ms (3.1%)

eval170.0ms (1.1%)

prune137.0ms (0.9%)

simplify498.0ms (3.4%)

localize357.0ms (2.4%)

series51.0ms (0.3%)

simplify389.0ms (2.6%)

rewrite316.0ms (2.1%)

eval407.0ms (2.8%)

prune193.0ms (1.3%)

regimes36.0ms (0.2%)

regimes31.0ms (0.2%)

regimes41.0ms (0.3%)

regimes27.0ms (0.2%)

regimes25.0ms (0.2%)

regimes23.0ms (0.2%)

regimes23.0ms (0.2%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

simplify12.0ms (0.1%)

soundness1.6s (11%)

preprocess171.0ms (1.2%)

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