Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze55.0ms (0.3%)

Memory

13.2MiB live, 89.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.7s (54.7%)

Memory

64.3MiB live, 10 840.5MiB allocated

Samples

4.0s	26 155×	0	invalid
3.4s	5 609×	2	valid
652.0ms	2 513×	1	valid
40.0ms	134×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-cos: 2.7s (44.2% of total)

const: 751.0ms (12.3% of total)

adjust: 484.0ms (7.9% of total)

ival-<: 391.0ms (6.4% of total)

ival-add: 383.0ms (6.3% of total)

ival-<=: 379.0ms (6.2% of total)

ival-mult: 331.0ms (5.4% of total)

ival-sub: 267.0ms (4.4% of total)

ival-fabs: 266.0ms (4.3% of total)

ival-and: 103.0ms (1.7% of total)

exact: 46.0ms (0.8% of total)

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

Bogosity

explain229.0ms (1.3%)

Memory

13.3MiB live, 484.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
132	1	(1.1458924791393156e-156 4.393344811072072e-167)	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	1	(1366.5626695677122 3.004712037506977e-13)	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	133	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	2

Confusion

	Predicted +	Predicted -
+	132	0
-	1	123

Precision

0.9924812030075187

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	0
-	1	0	123

Precision?

0.9924812030075187

Recall?

1.0

Freqs

test

number	freq
0	123
1	132
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

154.0ms	346×	2	valid
20.0ms	160×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 140.0ms

ival-cos: 109.0ms (77.9% of total)

adjust: 19.0ms (13.6% of total)

ival-sub: 7.0ms (5% of total)

ival-add: 4.0ms (2.9% of total)

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

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

preprocess36.0ms (0.2%)

Memory

-2.7MiB live, 74.8MiB allocated

Algorithm

1×	egg-herbie

Rules

108×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
80×	`associate--r+`
66×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

-23.1MiB live, 16.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize126.0ms (0.7%)

Memory

3.1MiB live, 203.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.06311401958404239	(cos.f64 (+.f64 x eps))
accuracy	29.692361242684626	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

104.0ms	173×	2	valid
11.0ms	80×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

ival-cos: 66.0ms (63.9% of total)

adjust: 33.0ms (31.9% of total)

ival-sub: 3.0ms (2.9% of total)

ival-add: 2.0ms (1.9% of total)

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

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

series4.0ms (0%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))>
#<alt (cos.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (cos.f64 x)>

Outputs
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

Calls

21 calls:

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

simplify308.0ms (1.7%)

Memory

-42.2MiB live, 505.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
4 148×	`lower-*.f64`
4 148×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite278.0ms (1.6%)

Memory

16.2MiB live, 494.1MiB allocated

Rules

4 936×	`lower-fma.f64`
4 936×	`lower-fma.f32`
4 656×	`lower-*.f64`
4 656×	`lower-*.f32`
2 192×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval39.0ms (0.2%)

Memory: -11.3MiB live, 104.1MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune106.0ms (0.6%)

Memory

30.9MiB live, 147.8MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	296	10	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	296	11	307

Accuracy

99.8%

Counts

307 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.6%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	52.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.5%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	52.3%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Compiler

Compiled 311 to 204 computations (34.4% saved)

simplify307.0ms (1.7%)

Memory

-18.6MiB live, 420.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
cost-diff	0	(neg.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	0	(*.f64 (sin.f64 x) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
cost-diff	0	(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
cost-diff	128	(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))
cost-diff	6208	(fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))

Rules

13 456×	`lower-fma.f32`
13 448×	`lower-fma.f64`
4 622×	`lower-*.f32`
4 598×	`lower-*.f64`
1 668×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	321
0	84	311
1	157	311
2	421	311
3	984	303
4	1802	303
5	3293	303
6	5164	303
7	6473	303
8	7935	303
0	8062	293

Stop Event

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

Calls

Call 1

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

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

localize350.0ms (2%)

Memory

20.6MiB live, 536.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.13000103364128757	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.140625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.2109375	(+.f64 x (+.f64 x eps))
accuracy	0.0078125	(fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
accuracy	0.06311401958404239	(cos.f64 (+.f64 x eps))
accuracy	0.7385323851000944	#s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
accuracy	29.692361242684626	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.01171875	(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy	12.861051099699774	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(cos.f64 eps)
accuracy	28.807970079630138	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	29.575134027615096	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.1015625	(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
accuracy	0.140625	(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
accuracy	0.3046875	(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
accuracy	0.359375	(*.f64 eps #s(literal 1/24 binary64))

Samples

190.0ms	173×	2	valid
98.0ms	80×	1	valid
5.0ms	2×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 273 to 47 computations (82.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 246.0ms

ival-cos: 134.0ms (54.5% of total)

adjust: 37.0ms (15% of total)

ival-mult: 32.0ms (13% of total)

ival-add: 20.0ms (8.1% of total)

ival-sin: 9.0ms (3.7% of total)

const: 7.0ms (2.8% of total)

ival-sub: 3.0ms (1.2% of total)

ival-neg: 2.0ms (0.8% of total)

exact: 1.0ms (0.4% of total)

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

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

series54.0ms (0.3%)

Memory

-25.5MiB live, 23.0MiB allocated

Counts

25 → 480

Calls

Call 1

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

Outputs
#<alt (sin (neg x))>
#<alt (+ (sin (neg x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt -1/2>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (* 1/24 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
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#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

120 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
2.0ms	x	@	-inf	(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
1.0ms	x	@	inf	(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	0	(* (sin x) (neg eps))

simplify345.0ms (1.9%)

Memory

-4.9MiB live, 190.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 148×	`lower-fma.f64`
13 148×	`lower-fma.f32`
7 562×	`lower-*.f64`
7 562×	`lower-*.f32`
3 874×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	4501
1	1484	4358
2	4204	4348
0	8728	4059

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 455

Calls

Call 1

Inputs
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
-1/2
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

Outputs
(sin (neg x))
(sin.f64 (neg.f64 x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.f64 (.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(.f64 eps (.f64 (.f64 eps eps) (-.f64 (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))) (/.f64 (sin.f64 x) (.f64 eps (*.f64 eps eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)) (neg.f64 (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(+.f64 #s(literal -1 binary64) (-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps))))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/6 binary64) (sin.f64 eps)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (neg.f64 (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
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(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(.f64 (sin.f64 x) (.f64 eps #s(literal 1/2 binary64)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* -1/36 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/36 binary64))) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/30240 binary64) #s(literal 1/720 binary64)) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps x))
(.f64 x (.f64 eps #s(literal 1/6 binary64)))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(.f64 x (fma.f64 x (.f64 x (.f64 eps #s(literal -1/36 binary64))) (.f64 eps #s(literal 1/6 binary64))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/720 binary64) (.f64 eps (.f64 x x))))) (.f64 eps #s(literal 1/6 binary64))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/30240 binary64) (.f64 eps #s(literal 1/720 binary64)))) (.f64 eps #s(literal -1/36 binary64))) (.f64 eps #s(literal 1/6 binary64))))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 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) (- (* 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))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite392.0ms (2.2%)

Memory

22.0MiB live, 250.2MiB allocated

Rules

4 636×	`lower-*.f32`
4 612×	`lower-*.f64`
4 114×	`lower-/.f64`
4 114×	`lower-/.f32`
3 290×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	241
0	84	235
1	302	235
2	2568	235
0	8712	226

Stop Event

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

Counts

25 → 570

Calls

Call 1

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

Outputs
(+.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))))
(+.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) eps)) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 eps eps) (sin.f64 (neg.f64 x))))
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) eps))) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (sin.f64 x))))
(-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))))
(fma.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))) (sin.f64 (neg.f64 x)))
(fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x)) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) eps) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))) eps (sin.f64 (neg.f64 x)))
(fma.f64 (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))))
(fma.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x)) eps (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (cos.f64 x) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(fma.f64 (.f64 eps (cos.f64 x)) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 eps eps) (sin.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
(/.f64 (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (neg.f64 (.f64 eps (sin.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (neg.f64 (.f64 eps (sin.f64 x))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (neg.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))) (.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))) (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (neg.f64 (neg.f64 (-.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 (neg.f64 x))))))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (sin.f64 (neg.f64 x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))))))
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(/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (-.f64 x x) (.f64 (neg.f64 eps) (-.f64 (.f64 x x) (.f64 x x)))) (*.f64 (neg.f64 eps) (-.f64 x x)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 (neg.f64 eps) (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))))) (.f64 (neg.f64 eps) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (-.f64 x x) (.f64 (neg.f64 eps) (-.f64 (.f64 x x) (.f64 x x)))) (*.f64 (neg.f64 eps) (-.f64 x x)))
(/.f64 (fma.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))))) (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 x x (-.f64 (.f64 x x) (*.f64 x x)))))
(/.f64 (fma.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (-.f64 x x) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 x x) (.f64 x x)))) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 x x)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (/.f64 eps (.f64 eps eps)) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (/.f64 eps (*.f64 eps eps))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (.f64 eps eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (*.f64 eps eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) eps (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 eps eps))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) eps))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (.f64 eps eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (*.f64 eps eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 (.f64 eps eps)) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (*.f64 eps eps))))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 1 binary64) eps) (.f64 (-.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 x x) (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (/.f64 eps (.f64 eps eps)) (.f64 (-.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 x x) (/.f64 eps (.f64 eps eps))))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps) (.f64 (-.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) eps (.f64 (-.f64 x x) (.f64 eps eps))) (*.f64 (-.f64 x x) eps))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps) (.f64 (-.f64 x x) (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 (-.f64 x x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 eps) (.f64 (-.f64 x x) (neg.f64 (.f64 eps eps)))) (*.f64 (-.f64 x x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 eps) (.f64 (-.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))) (*.f64 (-.f64 x x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 (.f64 eps eps)) (.f64 (-.f64 x x) (neg.f64 (.f64 eps (.f64 eps eps))))) (.f64 (-.f64 x x) (neg.f64 (.f64 eps eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 (-.f64 x eps) x)) (.f64 (-.f64 (-.f64 x eps) x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (-.f64 (-.f64 x eps) x) (-.f64 (-.f64 x eps) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 eps x) (+.f64 eps (-.f64 x x)) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (-.f64 x eps) x)))) (neg.f64 (neg.f64 (-.f64 (-.f64 x eps) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x))) (neg.f64 (+.f64 eps (-.f64 x x))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(pow.f64 (/.f64 (fma.f64 (+.f64 eps x) (+.f64 eps (-.f64 x x)) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (-.f64 x eps) x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (-.f64 x eps) x))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) (+.f64 eps (-.f64 x x)) (*.f64 x x))))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (-.f64 x eps) x)) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 x eps) x)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x))) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps x)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x))) (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 eps x) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 eps x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))

eval278.0ms (1.6%)

Memory: -19.3MiB live, 192.6MiB allocated
Compiler: Compiled 28 610 to 2 773 computations (90.3% saved)

prune165.0ms (0.9%)

Memory

6.4MiB live, 212.0MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 072	15	1 087
Fresh	3	2	5
Picked	4	1	5
Done	0	1	1
Total	1 079	19	1 098

Accuracy

100.0%

Counts

1 098 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.6%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
▶	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))
	70.8%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
▶	52.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
▶	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
▶	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Compiler

Compiled 821 to 435 computations (47% saved)

simplify405.0ms (2.3%)

Memory

10.7MiB live, 286.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
cost-diff	0	#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
cost-diff	64	(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
cost-diff	128	(fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))
cost-diff	320	(fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

16 890×	`lower-fma.f32`
16 870×	`lower-fma.f64`
4 566×	`lower-*.f32`
4 530×	`lower-*.f64`
3 550×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	710
0	131	712
1	274	675
2	766	638
3	2195	638
4	3022	638
5	5063	638
6	7416	638
0	8202	613

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
(+.f64 x x)
x
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))
x
(fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64))))
(fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))
eps
#s(literal 1/6 binary64)
(.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64))
(.f64 eps (.f64 x x))
(*.f64 x x)
#s(literal -1/120 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
x
(fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (cos.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)
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(sin.f64 x)
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
x
(+.f64 x x)
x
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(cos.f64 (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(cos.f64 x)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))
#s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))
(.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))))
x
(fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
#s(literal 1/6 binary64)
(.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64))
(.f64 eps (.f64 x x))
(*.f64 x x)
#s(literal -1/120 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64))))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64))))))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)))))
x
(fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal 1/6 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (.f64 eps #s(literal -1/36 binary64)))) (.f64 x #s(literal 1/6 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)

localize628.0ms (3.5%)

Memory

13.0MiB live, 769.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
accuracy	0.0078125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
accuracy	0.13000103364128757	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.140625	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	0.140625	(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
accuracy	0.359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.4134833946930315	(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.7233816852857962	#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy	0.09375	(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64))))
accuracy	0.3515625	(fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))
accuracy	0.6920263094926321	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))
accuracy	12.861051099699774	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
accuracy	0.3272129186447549	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	28.807970079630138	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	29.575134027615096	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
accuracy	0.0078125	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0234375	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.140625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

383.0ms	171×	2	valid
135.0ms	80×	1	valid
14.0ms	4×	3	valid
1.0ms	1×	0	valid

Compiler

Compiled 530 to 83 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 387.0ms

adjust: 120.0ms (31% of total)

ival-cos: 82.0ms (21.2% of total)

ival-mult: 80.0ms (20.7% of total)

ival-sin: 49.0ms (12.7% of total)

ival-add: 33.0ms (8.5% of total)

const: 16.0ms (4.1% of total)

ival-sub: 3.0ms (0.8% of total)

ival-neg: 2.0ms (0.5% of total)

exact: 1.0ms (0.3% of total)

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

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

series39.0ms (0.2%)

Memory

-19.1MiB live, 65.8MiB allocated

Counts

25 → 528

Calls

Call 1

Inputs
#<alt (*.f64 (+.f64 x x) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))>
#<alt (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))>
#<alt #s(approx (cos eps) #s(literal 1 binary64))>
#<alt (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))>
#<alt (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))>
#<alt #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))>
#<alt (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))>
#<alt (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))>
#<alt #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))>
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))>
#<alt (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))>
#<alt (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))>
#<alt (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))>
#<alt (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64))))>
#<alt (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))>
#<alt (*.f64 eps #s(literal 1/6 binary64))>
#<alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))>

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
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#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (* x (+ 1/6 (* -1/36 (pow eps 2))))>
#<alt (* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))>
#<alt (* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))>
#<alt (* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))>
#<alt (* x (+ 1/6 (* -1/36 (pow eps 2))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))>
#<alt (* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))>
#<alt (* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>

Calls

132 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2)))
5.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
2.0ms	eps	@	inf	(+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))
1.0ms	eps	@	inf	(+ (* eps 1/6) (* (* eps (* x x)) -1/120))
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

simplify284.0ms (1.6%)

Memory

3.6MiB live, 552.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 086×	`lower-fma.f64`
14 086×	`lower-fma.f32`
8 022×	`lower-*.f64`
8 022×	`lower-*.f32`
3 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	644	7195
1	2031	6934
2	6492	6933
0	8053	6405

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 504

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* -1 (* eps (- (* 1/120 (pow x 2)) 1/6)))
(* -1 (* eps (- (* 1/120 (pow x 2)) 1/6)))
(* -1 (* eps (- (* 1/120 (pow x 2)) 1/6)))
(* -1 (* eps (- (* 1/120 (pow x 2)) 1/6)))
(* 1/6 eps)
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)
(- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* -1 (* eps (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (+ (* -1/36 (pow eps 2)) (* 1/6 (/ (pow eps 2) (pow x 2)))))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 (/ (pow eps 2) x))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2)))) x)))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/6 (* eps x))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* -1/120 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))
(* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))
(* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))
(* -1 (* eps (* x (- (* 1/120 (pow x 2)) 1/6))))
(* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
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(.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(* x (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 (.f64 eps eps) #s(literal 1/36 binary64) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 (.f64 eps eps) #s(literal 1/36 binary64) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (/.f64 eps x)) (fma.f64 (.f64 eps eps) #s(literal 1/36 binary64) #s(literal -1/6 binary64))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 eps (fma.f64 x (.f64 #s(literal -1/36 binary64) eps) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(fma.f64 eps (fma.f64 eps (fma.f64 x #s(literal -1/36 binary64) (.f64 eps #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(* -1/48 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(.f64 (.f64 eps eps) (*.f64 eps (fma.f64 x (/.f64 #s(literal -1/36 binary64) eps) #s(literal -1/48 binary64))))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/48 binary64) (fma.f64 #s(literal -1/36 binary64) (/.f64 x eps) (/.f64 #s(literal 1/4 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/48 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))) (fma.f64 #s(literal -1/36 binary64) (/.f64 x eps) (/.f64 #s(literal 1/4 binary64) (.f64 eps eps))))))
(* -1/48 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(.f64 (fma.f64 (/.f64 x eps) #s(literal 1/36 binary64) #s(literal 1/48 binary64)) (neg.f64 (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(.f64 (.f64 eps (*.f64 eps eps)) (neg.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 (fma.f64 x #s(literal -1/36 binary64) (/.f64 #s(literal 1/4 binary64) eps)) eps))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 (-.f64 (.f64 x #s(literal -1/36 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (/.f64 x eps) #s(literal -1/4 binary64)) eps)) eps)) (neg.f64 (.f64 eps (.f64 eps 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))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite211.0ms (1.2%)

Memory

-5.4MiB live, 316.4MiB allocated

Rules

3 566×	`lower-fma.f32`
3 546×	`lower-fma.f64`
2 816×	`lower-*.f32`
2 782×	`lower-*.f64`
1 450×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	541
0	131	510
1	532	446
0	4835	438

Stop Event

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

Counts

25 → 341

Calls

Call 1

Inputs
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
(fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))
(fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps))))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (.f64 x x)) #s(literal -1/120 binary64))))
(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))
(*.f64 eps #s(literal 1/6 binary64))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Outputs
#s(literal 0 binary64)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (neg.f64 eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (neg.f64 eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (*.f64 x x))) #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 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x))
(fma.f64 (*.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) (.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) eps (*.f64 x x)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps (neg.f64 eps)) (neg.f64 eps))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 eps eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps)) (neg.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (neg.f64 eps))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (.f64 x x))))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
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(/.f64 (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (-.f64 (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (.f64 (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))))))) (neg.f64 (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))) (neg.f64 (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))))) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))))
(.f64 (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))))))
(.f64 (.f64 (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)))
(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) eps)
(/.f64 (.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)
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))

eval104.0ms (0.6%)

Memory: 4.2MiB live, 119.2MiB allocated
Compiler: Compiled 25 474 to 2 029 computations (92% saved)

prune88.0ms (0.5%)

Memory

9.1MiB live, 138.7MiB allocated

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	859	18	877
Fresh	7	5	12
Picked	4	1	5
Done	1	1	2
Total	871	25	896

Accuracy

100.0%

Counts

896 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	36.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
▶	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))
✓	52.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
▶	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
	33.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
▶	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
▶	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))

Compiler

Compiled 1 283 to 684 computations (46.7% saved)

simplify192.0ms (1.1%)

Memory

4.1MiB live, 80.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
cost-diff	0	#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
cost-diff	320	(fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
cost-diff	0	(.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
cost-diff	128	(fma.f64 (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))
cost-diff	0	(neg.f64 eps)
cost-diff	0	(*.f64 x (neg.f64 eps))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

13 020×	`lower-fma.f32`
12 996×	`lower-fma.f64`
3 688×	`lower-+.f32`
3 684×	`lower-+.f64`
3 302×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	990
0	164	996
1	367	963
2	1097	921
3	3199	921
4	4364	917
5	7547	917
0	8085	871

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
(+.f64 x x)
x
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(*.f64 eps #s(literal 1/3840 binary64))
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
(*.f64 x (neg.f64 eps))
x
(neg.f64 eps)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))
(.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))
x
(fma.f64 (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
(fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(*.f64 x #s(literal -1/120 binary64))
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
x
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(*.f64 x x)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/4 binary64)
#s(literal -1/2 binary64)
(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 x #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
eps
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (fma.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (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))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 x) (.f64 (cos.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)
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 x) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(sin.f64 x)
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
x
(+.f64 x x)
x
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 x))
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(cos.f64 x)
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
(*.f64 eps #s(literal 1/3840 binary64))
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
(*.f64 x (neg.f64 eps))
(*.f64 eps (neg.f64 x))
x
(neg.f64 eps)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))
#s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)))))
(.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))
(.f64 x (.f64 eps (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64))))
x
(fma.f64 (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))
(.f64 eps (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(.f64 x (.f64 eps (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)))
eps
(fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 x #s(literal -1/120 binary64))
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps #s(literal -1/2 binary64))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 x (fma.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))
x
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 x x)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
#s(literal 1/4 binary64)
#s(literal -1/2 binary64)
(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 x #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)

localize505.0ms (2.8%)

Memory

6.8MiB live, 169.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
accuracy	0.05389077972199129	#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
accuracy	0.13000103364128757	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.140625	(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	0.140625	(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
accuracy	0.29296875	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.359375	(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
accuracy	0.7233816852857962	#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
accuracy	0.09375	(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
accuracy	0.359375	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
accuracy	0.6920263094926321	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))
accuracy	12.861051099699774	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
accuracy	0	(*.f64 x (neg.f64 eps))
accuracy	0	(neg.f64 eps)
accuracy	1.3145228966034816	#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
accuracy	12.861051099699774	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
accuracy	0.0078125	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
accuracy	0.0234375	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
accuracy	0.08203125	(*.f64 eps #s(literal 1/3840 binary64))
accuracy	0.140625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))

Samples

281.0ms	169×	2	valid
98.0ms	82×	1	valid
10.0ms	2×	3	valid
2.0ms	3×	0	valid

Compiler

Compiled 575 to 107 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 328.0ms

ival-mult: 101.0ms (30.8% of total)

adjust: 73.0ms (22.3% of total)

ival-cos: 55.0ms (16.8% of total)

ival-add: 44.0ms (13.4% of total)

const: 30.0ms (9.1% of total)

ival-sin: 18.0ms (5.5% of total)

ival-sub: 3.0ms (0.9% of total)

ival-neg: 2.0ms (0.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series29.0ms (0.2%)

Memory

-30.8MiB live, 12.2MiB allocated

Counts

28 → 600

Calls

Call 1

Inputs
#<alt (*.f64 (+.f64 x x) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))>
#<alt #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))>
#<alt (*.f64 x (neg.f64 eps))>
#<alt (neg.f64 eps)>
#<alt (fma.f64 (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))>
#<alt #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))>
#<alt (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))>
#<alt (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))>
#<alt (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))>
#<alt #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))>
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))>
#<alt (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))>
#<alt #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))>
#<alt (*.f64 eps #s(literal 1/3840 binary64))>
#<alt (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))>
#<alt (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))>
#<alt (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))>
#<alt (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))>
#<alt (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))>

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps x))>
#<alt (* -1 (* eps x))>
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#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* 1/6 eps)>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (* -1/120 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* 1/6 eps)>
#<alt (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (* -1/36 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/36 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>

Calls

150 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	inf	(* x (* eps (+ (* x (* x -1/120)) 1/6)))
1.0ms	eps	@	0	(+ (* (* x (* eps (+ (* x (* x -1/120)) 1/6))) x) (neg eps))
1.0ms	eps	@	0	(+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2))
0.0ms	eps	@	inf	(* x (neg eps))
0.0ms	eps	@	0	(* x (neg eps))

simplify222.0ms (1.2%)

Memory

29.4MiB live, 103.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 234×	`lower-fma.f64`
10 234×	`lower-fma.f32`
7 932×	`lower-*.f64`
7 932×	`lower-*.f32`
2 136×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	532	7341
1	1719	6993
2	5384	6979
0	8627	6478

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 576

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
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(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* -1 (* eps (sin x)))
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(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
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(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
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(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
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(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
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(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
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(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps x))
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(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
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(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)
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(* (pow x 3) (+ (* -1/36 eps) (* 1/4 (/ 1 x))))
(* (pow x 3) (+ (* -1/36 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ 1 x)))))
(* (pow x 3) (- (+ (* -1/36 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ 1 x)))) (* 1/2 (/ 1 (pow x 3)))))
(* -1/36 (* eps (pow x 3)))
(* -1 (* (pow x 3) (- (* 1/36 eps) (* 1/4 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ eps x))) x)) (* 1/36 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ 1/4 (* -1 (/ (+ (* -1/6 eps) (* 1/2 (/ 1 x))) x))) x)) (* 1/36 eps))))
(- (* 1/4 (pow x 2)) 1/2)
(- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)
(- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)
(- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)
(* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* eps (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* eps (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* eps (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))
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(* -1 (* eps (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)))))
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(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* 1/6 eps)
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* 1/6 (* eps x))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* -1/120 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* eps (+ 1/6 (* -1/36 (pow x 2))))
(* 1/6 eps)
(+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))
(* -1/36 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/36 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 (neg.f64 x))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 eps #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 x x)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
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(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps))
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(* -1/36 (* eps (pow x 2)))
(.f64 (.f64 eps (*.f64 x x)) #s(literal -1/36 binary64))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* -1/36 (* eps (pow x 2)))
(.f64 (.f64 eps (*.f64 x x)) #s(literal -1/36 binary64))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* (pow x 2) (+ (* -1/36 eps) (* 1/6 (/ eps (pow x 2)))))
(.f64 x (.f64 x (fma.f64 eps #s(literal -1/36 binary64) (.f64 #s(literal 1/6 binary64) (/.f64 eps (.f64 x x))))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/8 binary64) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite247.0ms (1.4%)

Memory

-15.7MiB live, 105.0MiB allocated

Rules

5 200×	`lower-fma.f32`
5 176×	`lower-fma.f64`
4 848×	`lower-*.f32`
4 808×	`lower-*.f64`
2 282×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	724
0	164	714
1	698	668
2	6632	661
0	8554	626

Stop Event

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

Counts

28 → 370

Calls

Call 1

Inputs
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
(*.f64 x (neg.f64 eps))
(neg.f64 eps)
(fma.f64 (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps))))
(.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))
(fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(*.f64 eps #s(literal 1/3840 binary64))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Outputs
#s(literal 0 binary64)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (neg.f64 eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (neg.f64 eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (+.f64 x eps) eps))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) x)
(fma.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)))) (neg.f64 x))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 x x (*.f64 (+.f64 x eps) eps)))
(/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) (.f64 (fma.f64 x x (*.f64 (+.f64 x eps) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps (neg.f64 eps)) (neg.f64 eps))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 eps eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps)) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x eps) eps))))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps)
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (neg.f64 eps))
(pow.f64 (/.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) (.f64 (fma.f64 x x (*.f64 (+.f64 x eps) eps)) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (+.f64 x eps) eps))))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) #s(literal -2 binary64)))
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(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x (.f64 x #s(literal -1/36 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64)) #s(literal 1/216 binary64))) (.f64 eps (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/216 binary64))))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/36 binary64))) (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal -1/6 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x #s(literal -1/36 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64)) #s(literal 1/216 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/216 binary64)))) (.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x #s(literal -1/36 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64)) #s(literal 1/216 binary64)) (.f64 eps eps)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/216 binary64)))) eps))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/36 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal -1/6 binary64)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/36 binary64)) (.f64 eps eps)) (.f64 (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal -1/6 binary64)) eps))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 eps #s(literal 1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64))) (.f64 (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) (.f64 eps #s(literal 1/6 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps))) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x #s(literal -1/36 binary64)) eps)) (.f64 eps #s(literal 1/6 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 x (.f64 x #s(literal -1/36 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64)) #s(literal 1/216 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/216 binary64)))))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/36 binary64))) (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal -1/6 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64))) eps)
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x #s(literal -1/36 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64)) #s(literal 1/216 binary64)) eps) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/216 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/36 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal -1/6 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) eps)
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))) (.f64 (cos.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))

eval102.0ms (0.6%)

Memory: 10.3MiB live, 84.4MiB allocated
Compiler: Compiled 26 942 to 2 006 computations (92.6% saved)

prune88.0ms (0.5%)

Memory

-1.8MiB live, 87.2MiB allocated

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	970	10	980
Fresh	6	12	18
Picked	3	2	5
Done	0	2	2
Total	979	26	1 005

Accuracy

100.0%

Counts

1 005 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	36.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
✓	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))
✓	52.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
	33.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	16.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
	78.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
	70.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
✓	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))

Compiler

Compiled 1 865 to 604 computations (67.6% saved)

regimes42.0ms (0.2%)

Memory

-19.1MiB live, 19.6MiB allocated

Counts

54 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.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))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

15.0ms	x
13.0ms	eps
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

49 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.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))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.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))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(approx (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (*.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))

Calls

3 calls:

12.0ms	x
12.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory

-22.0MiB live, 17.6MiB allocated

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps) (neg.f64 (*.f64 eps (sin.f64 x)))))

Outputs

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

Calls

3 calls:

12.0ms	x
12.0ms	eps
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

45 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps #s(approx (* 1/6 (sin x)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (neg.f64 x)))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

10.0ms	x
9.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Memory

-28.3MiB live, 15.0MiB allocated

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) (sin.f64 (neg.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

13.0ms	eps
9.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/24 binary64)) (/.f64 (fma.f64 x (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 (.f64 eps (*.f64 eps eps))))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-27.5MiB live, 12.0MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps (fma.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (.f64 x (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 x x (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x (+.f64 x eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))

Calls

3 calls:

8.0ms	eps
7.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (.f64 #s(literal -1/36 binary64) (.f64 eps (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`
98.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 eps (*.f64 x x)) #s(literal -1/120 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (.f64 x (.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( x (* x (+ (* eps 1/6) (* (* eps (* x x)) -1/120)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x #s(approx (+ (* eps 1/6) (* (* eps (* x x)) -1/120)) (.f64 #s(literal -1/120 binary64) (.f64 eps (*.f64 x x))))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (.f64 eps (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) x (neg.f64 eps)))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (-.f64 (-.f64 x eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (/.f64 (.f64 eps (neg.f64 eps)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.2%	1	`x`
79.2%	1	`eps`
79.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

-35.0MiB live, 4.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.1%	1	`eps`
79.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.1%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
52.2%	1	`eps`
52.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
52.2%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify15.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×	egg-herbie

Rules

92×	`*-commutative_binary64`
12×	`+-commutative_binary64`
8×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	192	912
1	246	912
2	258	912
3	267	912
4	271	912

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))

Outputs
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx ( (cos (* (+ x x) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #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))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x #s(approx (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps))) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (fma.f64 eps #s(approx (+ (* x (* eps (+ (* (* x x) -1/36) 1/6))) (+ (* 1/4 (* x x)) -1/2)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* x (+ (* (* eps eps) -1/36) 1/6)) (* (+ (* 1/24 (* eps eps)) -1/2) (* -1/2 eps)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))

soundness1.4s (7.8%)

Memory

-6.3MiB live, 33.2MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
14 086×	`lower-fma.f64`
14 086×	`lower-fma.f32`
13 148×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	644	7195
1	2031	6934
2	6492	6933
0	8053	6405
0	532	7341
1	1719	6993
2	5384	6979
0	8627	6478
0	110	724
0	164	714
1	698	668
2	6632	661
0	8554	626
0	485	4501
1	1484	4358
2	4204	4348
0	8728	4059
0	49	241
0	84	235
1	302	235
2	2568	235
0	8712	226
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

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

Compiler

Compiled 692 to 315 computations (54.5% saved)

preprocess95.0ms (0.5%)

Memory: 8.9MiB live, 87.2MiB allocated
Compiler: Compiled 790 to 252 computations (68.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze55.0ms (0.3%)

sample9.7s (54.7%)

explain229.0ms (1.3%)

preprocess36.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize126.0ms (0.7%)

series4.0ms (0%)

simplify308.0ms (1.7%)

rewrite278.0ms (1.6%)

eval39.0ms (0.2%)

prune106.0ms (0.6%)

simplify307.0ms (1.7%)

localize350.0ms (2%)

series54.0ms (0.3%)

simplify345.0ms (1.9%)

rewrite392.0ms (2.2%)

eval278.0ms (1.6%)

prune165.0ms (0.9%)

simplify405.0ms (2.3%)

localize628.0ms (3.5%)

series39.0ms (0.2%)

simplify284.0ms (1.6%)

rewrite211.0ms (1.2%)

eval104.0ms (0.6%)

prune88.0ms (0.5%)

simplify192.0ms (1.1%)

localize505.0ms (2.8%)

series29.0ms (0.2%)

simplify222.0ms (1.2%)

rewrite247.0ms (1.4%)

eval102.0ms (0.6%)

prune88.0ms (0.5%)

regimes42.0ms (0.2%)

regimes36.0ms (0.2%)

regimes36.0ms (0.2%)

regimes33.0ms (0.2%)

regimes29.0ms (0.2%)

regimes32.0ms (0.2%)

regimes26.0ms (0.1%)

regimes22.0ms (0.1%)

regimes22.0ms (0.1%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify15.0ms (0.1%)

soundness1.4s (7.8%)

preprocess95.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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