Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze50.0ms (0.3%)

Memory

-30.9MiB live, 62.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.9s (57.2%)

Memory

-105.8MiB live, 11 203.2MiB allocated

Samples

4.1s	26 541×	0	invalid
3.5s	5 671×	2	valid
702.0ms	2 466×	1	valid
15.0ms	119×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.3s

ival-cos: 3.1s (48.3% of total)

const: 945.0ms (14.9% of total)

adjust: 450.0ms (7.1% of total)

ival-add: 431.0ms (6.8% of total)

ival-mult: 294.0ms (4.6% of total)

ival-fabs: 282.0ms (4.4% of total)

ival-sub: 253.0ms (4% of total)

ival-<=: 242.0ms (3.8% of total)

ival-<: 210.0ms (3.3% of total)

ival-and: 105.0ms (1.7% of total)

exact: 53.0ms (0.8% of total)

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

Bogosity

explain195.0ms (1.1%)

Memory

25.1MiB live, 139.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
136	119	(2.0419021844044626e-177 5.1730854343917766e-191)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
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	255	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	137	0
-	119	0

Precision

0.53515625

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	137	0	0
-	119	0	0

Precision?

0.53515625

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

136.0ms	368×	2	valid
17.0ms	138×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 69 to 28 computations (59.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-cos: 99.0ms (76.9% of total)

adjust: 17.0ms (13.2% of total)

ival-sub: 9.0ms (7% of total)

ival-add: 3.0ms (2.3% of total)

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

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

preprocess30.0ms (0.2%)

Memory

-25.0MiB live, 19.4MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

5.9MiB live, 5.9MiB 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)

localize83.0ms (0.5%)

Memory

19.0MiB live, 58.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.056858544539389745	(cos.f64 (+.f64 x eps))
accuracy	30.555999228948973	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

66.0ms	184×	2	valid
8.0ms	69×	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: 62.0ms

ival-cos: 49.0ms (78.4% of total)

adjust: 9.0ms (14.4% of total)

ival-sub: 3.0ms (4.8% of total)

ival-add: 2.0ms (3.2% of total)

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

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

series3.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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	x	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	eps	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

simplify284.0ms (1.6%)

Memory

-22.7MiB live, 292.4MiB 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)

rewrite262.0ms (1.5%)

Memory

17.6MiB live, 371.0MiB 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))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #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)) (.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x))))))
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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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (.f64 eps (+.f64 x eps))) (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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (.f64 (-.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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.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 x x (.f64 eps (+.f64 x eps))) (-.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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 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 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (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))

eval118.0ms (0.7%)

Memory: -9.6MiB live, 28.0MiB allocated
Compiler: Compiled 8 023 to 876 computations (89.1% saved)

prune34.0ms (0.2%)

Memory

36.9MiB live, 36.9MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	297	9	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Accuracy

99.8%

Counts

307 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	51.5%	(-.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))))
	51.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.6%	(.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))
▶	51.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.6%	#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 281 to 186 computations (33.8% saved)

simplify375.0ms (2.2%)

Memory

-43.1MiB live, 327.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

20 080×	`lower-fma.f32`
20 072×	`lower-fma.f64`
4 406×	`lower-*.f32`
4 384×	`lower-*.f64`
2 154×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	279
0	77	269
1	139	269
2	346	269
3	707	261
4	968	261
5	1660	261
6	4034	261
7	5918	261
0	8168	256

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

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

localize267.0ms (1.5%)

Memory

18.2MiB live, 174.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(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))))
accuracy	0.10546875	(.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)))))
accuracy	0.22423758666392343	#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))))))
accuracy	0.3359375	(*.f64 eps #s(literal 1/6 binary64))
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	0.056858544539389745	(cos.f64 (+.f64 x eps))
accuracy	0.6811462142787427	#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	30.555999228948973	(-.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	12.557572864164625	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(cos.f64 eps)
accuracy	29.60031401176116	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	30.3935745281144	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.02734375	(.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	0.049470497205265515	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.109375	(.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	0.22265625	(+.f64 x (+.f64 x eps))

Samples

185.0ms	190×	2	valid
32.0ms	63×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 238 to 43 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-cos: 79.0ms (44.8% of total)

ival-mult: 34.0ms (19.3% of total)

adjust: 32.0ms (18.2% of total)

ival-add: 13.0ms (7.4% of total)

ival-sin: 6.0ms (3.4% of total)

const: 6.0ms (3.4% of total)

ival-sub: 3.0ms (1.7% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series29.0ms (0.2%)

Memory

-8.9MiB live, 27.7MiB allocated

Counts

23 → 444

Calls

Call 1

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

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<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)) (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 (- (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 (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<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 x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<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)>
#<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 (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<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))))>
#<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 (* 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)>

Calls

111 calls:

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

simplify325.0ms (1.9%)

Memory

-2.3MiB live, 318.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 872×	`lower-fma.f64`
13 872×	`lower-fma.f32`
6 234×	`lower-*.f64`
6 234×	`lower-*.f32`
4 334×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	407	4024
1	1229	3839
2	3410	3785
0	8042	3537

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 419

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -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)))))
(- (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)))
(* -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)
(- (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 (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
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))))
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)))))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)

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

rewrite279.0ms (1.6%)

Memory

17.6MiB live, 361.4MiB allocated

Rules

4 376×	`lower-/.f64`
4 376×	`lower-/.f32`
4 306×	`lower-*.f32`
4 284×	`lower-*.f64`
3 608×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	210
0	77	204
1	272	204
2	2209	204
0	8271	199

Stop Event

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

Counts

23 → 649

Calls

Call 1

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

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

eval159.0ms (0.9%)

Memory: -18.1MiB live, 244.1MiB allocated
Compiler: Compiled 30 652 to 3 058 computations (90% saved)

prune111.0ms (0.6%)

Memory

6.5MiB live, 170.8MiB allocated

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	1 121	20	1 141
Fresh	3	1	4
Picked	3	2	5
Done	0	1	1
Total	1 127	24	1 151

Accuracy

100.0%

Counts

1 151 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	99.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (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)))) #s(literal -2 binary64))
	32.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))))
▶	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	81.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
	11.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))
✓	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.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))))))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) (.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))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))

Compiler

Compiled 915 to 554 computations (39.5% saved)

simplify333.0ms (1.9%)

Memory

4.5MiB live, 201.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
cost-diff	0	#s(approx (* -1/2 (cos x)) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 eps #s(approx (* -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
cost-diff	192	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 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	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Rules

15 076×	`lower-fma.f32`
15 062×	`lower-fma.f64`
3 952×	`lower-*.f32`
3 928×	`lower-*.f64`
2 084×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	475
0	102	448
1	178	448
2	477	448
3	1274	433
4	2169	433
5	3211	433
6	5550	433
0	8111	425

Stop Event

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

Calls

Call 1

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

localize387.0ms (2.2%)

Memory

-22.1MiB live, 102.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.049470497205265515	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.10546875	(.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.22265625	(+.f64 x (+.f64 x eps))
accuracy	0.1015625	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
accuracy	0.22423758666392343	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
accuracy	0.3359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.8302908844145122	#s(approx (* -1/2 (cos x)) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
accuracy	0.00390625	(.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))
accuracy	0.1015625	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
accuracy	0.22423758666392343	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
accuracy	1.0321899582231593	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
accuracy	0.3528828536587368	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	29.296721628315108	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	30.060617045618784	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.0234375	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
accuracy	0.049470497205265515	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.10546875	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))

Samples

254.0ms	188×	2	valid
40.0ms	63×	1	valid
3.0ms	2×	5	exit
1.0ms	3×	0	valid

Compiler

Compiled 354 to 55 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

ival-cos: 76.0ms (33.8% of total)

adjust: 42.0ms (18.7% of total)

ival-mult: 41.0ms (18.2% of total)

ival-sin: 32.0ms (14.2% of total)

ival-add: 19.0ms (8.4% of total)

ival-div: 6.0ms (2.7% of total)

const: 4.0ms (1.8% of total)

ival-sub: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series15.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

24 → 504

Calls

Call 1

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

Outputs
#<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 (- (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 (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))>
#<alt (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))) (/ 1 x)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<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 (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
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#<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

126 calls:

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

simplify451.0ms (2.6%)

Memory

26.3MiB live, 183.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 636×	`lower-fma.f64`
15 636×	`lower-fma.f32`
6 642×	`lower-*.f64`
6 642×	`lower-*.f32`
4 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	412	6069
1	1249	5753
2	3472	5639
0	8139	5217

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 486

Calls

Call 1

Inputs
(* -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))
(- (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)
(* -1 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 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 (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(- (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 (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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)))
(* -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)))))
(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)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(* -1 x)
(+ (* -1 x) (* 1/4 (* eps (pow x 2))))
(+ (* -1 x) (* eps (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2)))))
(+ (* -1 x) (* eps (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2)))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/4 (pow x 2)) (/ x eps)) eps)) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/4 (pow x 2)) (/ x eps)) eps)) (* 1/6 x)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
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
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (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 (.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 (+ (* -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 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(* -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)))
(* -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)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (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 (.f64 #s(literal -2 binary64) (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 x (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #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 x (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #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)))
(* -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)))
(* -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)))
(* -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 eps (.f64 (sin.f64 x) #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)))))
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(*.f64 eps #s(literal 1/6 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 (* 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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #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 (.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 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 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(+ (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 (* 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))

rewrite269.0ms (1.6%)

Memory

-13.8MiB live, 303.7MiB allocated

Rules

3 880×	`lower-fma.f32`
3 866×	`lower-fma.f64`
3 642×	`lower-/.f32`
3 638×	`lower-/.f64`
3 582×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	380
0	102	364
1	374	364
2	3330	364
0	8293	354

Stop Event

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

Counts

24 → 484

Calls

Call 1

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

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

eval110.0ms (0.6%)

Memory: 1.1MiB live, 197.2MiB allocated
Compiler: Compiled 25 284 to 2 135 computations (91.6% saved)

prune100.0ms (0.6%)

Memory

-14.7MiB live, 228.9MiB allocated

Pruning

32 alts after pruning (28 fresh and 4 done)

	Pruned	Kept	Total
New	948	22	970
Fresh	10	6	16
Picked	3	2	5
Done	1	2	3
Total	962	32	994

Accuracy

100.0%

Counts

994 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (+ (* 1/2 eps) 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))))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
▶	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 eps eps))))
	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
✓	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	81.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
✓	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.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 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
	50.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
▶	95.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
	51.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))

Compiler

Compiled 1 304 to 749 computations (42.6% saved)

simplify339.0ms (1.9%)

Memory

-0.8MiB live, 520.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
cost-diff	128	(-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))
cost-diff	704	(.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
cost-diff	192	(fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Rules

18 472×	`lower-fma.f32`
18 454×	`lower-fma.f64`
5 370×	`lower-*.f32`
5 340×	`lower-*.f64`
1 836×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	922
0	118	914
1	240	914
2	647	898
3	1719	886
4	2964	886
5	5249	881
0	8288	839

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(*.f64 eps eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))
(neg.f64 x)
x
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
x
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))
(*.f64 eps eps)
(fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))
x
#s(literal 1/6 binary64)
(/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)
(-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))
#s(literal -1/2 binary64)
(fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))
(*.f64 x #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(/.f64 x eps)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal -2 binary64)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.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 ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(*.f64 eps eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))
(neg.f64 x)
x
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
x
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)))))))
eps
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))))))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))
(.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))))
(*.f64 eps eps)
(fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))
(fma.f64 x #s(literal 1/6 binary64) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))
x
#s(literal 1/6 binary64)
(/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))
(fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))
(*.f64 x #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(/.f64 x eps)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#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 ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
#s(approx (sin (* 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)

localize379.0ms (2.2%)

Memory

34.8MiB live, 306.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
accuracy	0.049470497205265515	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.109375	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.11794141944377298	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
accuracy	0.22423758666392343	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
accuracy	0.2421875	(/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)
accuracy	1.0321899582231593	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))
accuracy	30.038003960628664	(.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))
accuracy	0.10546875	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.22423758666392343	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
accuracy	0.3359375	(*.f64 eps #s(literal 1/6 binary64))
accuracy	1.0315537303578748	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
accuracy	0.10546875	(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
accuracy	0.22423758666392343	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
accuracy	1.0321899582231593	#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
accuracy	24.004211201871875	#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))
accuracy	0.02734375	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
accuracy	0.049470497205265515	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.109375	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.33203125	(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))

Samples

231.0ms	175×	2	valid
64.0ms	77×	1	valid
2.0ms	3×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 510 to 72 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 245.0ms

adjust: 62.0ms (25.3% of total)

ival-mult: 61.0ms (24.9% of total)

ival-cos: 51.0ms (20.8% of total)

ival-add: 29.0ms (11.8% of total)

const: 18.0ms (7.4% of total)

ival-sin: 10.0ms (4.1% of total)

ival-div: 6.0ms (2.5% of total)

ival-sub: 5.0ms (2% of total)

exact: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

series26.0ms (0.2%)

Memory

-34.8MiB live, 9.4MiB allocated

Counts

25 → 552

Calls

Call 1

Inputs
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))>
#<alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))>
#<alt (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))>
#<alt #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))>
#<alt #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))>
#<alt (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))>
#<alt (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))>
#<alt #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))>
#<alt (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))>
#<alt (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))>
#<alt (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))))>
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))>
#<alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))>
#<alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))>
#<alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (*.f64 eps #s(literal 1/6 binary64))>
#<alt #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))>
#<alt (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)>

Outputs
#<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 (- (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)))>
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#<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 (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<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 (* -1/48 eps)>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 5))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<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)))>
#<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 (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (/ -1/2 eps)>
#<alt (- (* -1 (/ x (pow eps 2))) (* 1/2 (/ 1 eps)))>
#<alt (- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))>
#<alt (- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))>
#<alt (* 1/4 (/ (pow x 2) eps))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))>
#<alt (* 1/4 (/ (pow x 2) eps))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))>
#<alt (* -1 (/ x (pow eps 2)))>
#<alt (/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))>
#<alt (/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))>
#<alt (/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))>
#<alt (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))>
#<alt (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)>
#<alt (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)>
#<alt (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)>
#<alt (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))>
#<alt (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))>
#<alt (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))>
#<alt (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))>

Calls

138 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps)))
1.0ms	x	@	inf	(* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps)))
1.0ms	eps	@	0	(* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps)))
0.0ms	eps	@	inf	(* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps)))
0.0ms	eps	@	inf	(* eps (+ (* (* eps eps) (+ (* (* eps eps) -1/645120) 1/3840)) -1/48))

simplify344.0ms (2%)

Memory

13.2MiB live, 177.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 318×	`lower-fma.f64`
14 318×	`lower-fma.f32`
7 204×	`lower-*.f64`
7 204×	`lower-*.f32`
3 336×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	459	7744
1	1387	7321
2	3944	7183
0	8759	6659

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

Inputs
(* -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))))))))))
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-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (/ 1 (* eps x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (/ 1 (* eps x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(* -1 (/ x eps))
(/ (- (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2))))) x) eps)
(/ (- (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2))))) x) eps)
(/ (- (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2))))) x) eps)
(* -1 (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (pow x 2))))
(* -1 (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (pow x 2))))
(- (* -1 (/ x eps)) (+ 1/2 (* -1/4 (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)
(- (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 (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -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))
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 5))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 5))
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(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)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(/ -1/2 eps)
(- (* -1 (/ x (pow eps 2))) (* 1/2 (/ 1 eps)))
(- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))
(- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))
(* 1/4 (/ (pow x 2) eps))
(* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(* 1/4 (/ (pow x 2) eps))
(* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(* -1 (/ x (pow eps 2)))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))

Outputs
(* -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 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.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 eps (fma.f64 (.f64 eps (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))) (neg.f64 (sin.f64 x))))
(* -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)))
(* -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)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (- (* 2 x) (* -1 eps))))))
(.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 (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))))))
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(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(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 #s(literal -1/48 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 (cos.f64 x) #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 (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 (+ 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))
(* 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))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 eps (.f64 eps (-.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 eps (.f64 eps (-.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 eps x) #s(literal -1/2 binary64))) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
(- (* -1 (/ x (pow eps 2))) (* 1/2 (/ 1 eps)))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 1/4 binary64) eps) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) eps))
(- (* x (- (* 1/4 (/ x eps)) (/ 1 (pow eps 2)))) (* 1/2 (/ 1 eps)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 1/4 binary64) eps) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) eps))
(* 1/4 (/ (pow x 2) eps))
(/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) eps)
(* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps x))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) x))))
(* 1/4 (/ (pow x 2) eps))
(/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) eps)
(* (pow x 2) (- (* 1/4 (/ 1 eps)) (/ 1 (* (pow eps 2) x))))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps x))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (/ 1 (pow eps 2))) x)) (* 1/4 (/ 1 eps))))
(.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) eps) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) x))))
(* -1 (/ x (pow eps 2)))
(/.f64 x (*.f64 eps (neg.f64 eps)))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(/.f64 (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x) (*.f64 eps eps))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(/.f64 (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x) (*.f64 eps eps))
(/ (+ (* -1 x) (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))) (pow eps 2))
(/.f64 (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x) (*.f64 eps eps))
(* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) eps)
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))) eps)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) eps)
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)
(* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)

rewrite253.0ms (1.5%)

Memory

22.2MiB live, 135.5MiB allocated

Rules

4 864×	`lower-fma.f32`
4 846×	`lower-fma.f64`
4 788×	`lower-*.f32`
4 758×	`lower-*.f64`
2 736×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	734
0	118	726
1	488	726
2	4612	726
0	8469	692

Stop Event

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

Counts

25 → 260

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
#s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))
(fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))
(-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 eps #s(literal 1/6 binary64))
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.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 ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.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 ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(+.f64 (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(fma.f64 #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(+.f64 (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) #s(literal 0 binary64)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) #s(literal 0 binary64)))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(fma.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) eps (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) #s(literal 0 binary64)))
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(fma.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) #s(literal 0 binary64) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
(/.f64 (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
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(/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))) eps)
(.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))))
(.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x))) eps)
#s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))
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(fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (+.f64 (neg.f64 x) (*.f64 eps #s(literal -1/2 binary64))))
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(.f64 (pow.f64 (/.f64 eps (-.f64 #s(literal -1/8 binary64) (.f64 (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)) (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 eps (-.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps)) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal -1/2 binary64))))

eval91.0ms (0.5%)

Memory: -12.1MiB live, 70.0MiB allocated
Compiler: Compiled 19 954 to 1 418 computations (92.9% saved)

prune76.0ms (0.4%)

Memory

-3.6MiB live, 74.6MiB allocated

Pruning

34 alts after pruning (26 fresh and 8 done)

	Pruned	Kept	Total
New	834	12	846
Fresh	9	14	23
Picked	1	4	5
Done	0	4	4
Total	844	34	878

Accuracy

100.0%

Counts

878 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
✓	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))))
	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
✓	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	81.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
✓	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.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 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
✓	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
	52.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
	95.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
	51.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
	50.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))

Compiler

Compiled 1 920 to 677 computations (64.7% saved)

regimes45.0ms (0.3%)

Memory

-22.9MiB live, 21.8MiB allocated

Counts

64 → 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(-.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 ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.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)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x 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))) (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)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #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 (/.f64 #s(literal 1 binary64) eps) (/.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.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)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 x) (cos.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 #s(literal 1/2 binary64) eps)) #s(approx (sin (+ (* 1/2 eps) 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))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (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)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

15.0ms	x
14.0ms	eps
12.0ms	(-.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)

regimes35.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

50 → 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(-.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 ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.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)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))

Outputs

(*.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

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)

regimes32.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(-.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 ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.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)) (fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

11.0ms	x
10.0ms	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)

regimes31.0ms (0.2%)

Memory

-22.6MiB live, 16.5MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

40 → 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(-.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 (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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
99.3%	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)

regimes27.0ms (0.2%)

Memory

-24.7MiB live, 14.7MiB 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 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))))

Outputs

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

Calls

3 calls:

10.0ms	x
9.0ms	eps
7.0ms	(-.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)

regimes23.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

8.0ms	eps
8.0ms	x
6.0ms	(-.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)

regimes22.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

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

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 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
98.5%	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)

regimes20.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB 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 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) #s(approx (* (* eps eps) (+ (* x 1/6) (/ (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) eps))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(approx (- -1/2 (+ (* x (* x -1/4)) (/ x eps))) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 eps (fma.f64 x #s(literal 1/4 binary64) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (fma.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps (.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* eps -1/2) (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1))) (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (/.f64 x eps))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/6 binary64) x) (fma.f64 eps #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))

Outputs

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

Calls

3 calls:

7.0ms	x
7.0ms	eps
5.0ms	(-.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)

regimes20.0ms (0.1%)

Memory

-28.4MiB live, 11.4MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

7.0ms	x
6.0ms	eps
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

3.0ms	x
3.0ms	eps
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

4.7MiB 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 eps (neg.f64 x))))

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

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

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.7%	1	`x`
79.7%	1	`eps`
79.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 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
51.1%	1	`x`
51.1%	1	`eps`
51.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Rules

82×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	547
1	189	547
2	196	547
3	201	547
4	204	547
5	205	547

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#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)))

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #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))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 #s(literal 1/2 binary64) eps 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 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (.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 ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64))) (.f64 eps #s(literal 1/4 binary64)))) (.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x (.f64 #s(literal -1/6 binary64) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) #s(literal -1/6 binary64))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 x (fma.f64 x (.f64 x (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)))) (fma.f64 eps (fma.f64 eps #s(literal 1/6 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) #s(approx (+ (* x (+ (* eps (* eps 1/6)) -1)) (* eps -1/2)) (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))) (fma.f64 eps #s(literal -1/2 binary64) #s(approx (* x (+ (* eps (+ (* eps 1/6) (* x 1/4))) -1)) (neg.f64 x))))))
#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))))

soundness1.2s (7.1%)

Memory

-15.0MiB live, 26.6MiB allocated

Rules

15 636×	`lower-fma.f64`
15 636×	`lower-fma.f32`
14 318×	`lower-fma.f64`
14 318×	`lower-fma.f32`
14 158×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	407	4024
1	1229	3839
2	3410	3785
0	8042	3537
0	459	7744
1	1387	7321
2	3944	7183
0	8759	6659
0	412	6069
1	1249	5753
2	3472	5639
0	8139	5217
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Compiler

Compiled 439 to 220 computations (49.9% saved)

preprocess119.0ms (0.7%)

Memory: -3.6MiB live, 74.2MiB allocated
Compiler: Compiled 612 to 228 computations (62.7% 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%)

analyze50.0ms (0.3%)

sample9.9s (57.2%)

explain195.0ms (1.1%)

preprocess30.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize83.0ms (0.5%)

series3.0ms (0%)

simplify284.0ms (1.6%)

rewrite262.0ms (1.5%)

eval118.0ms (0.7%)

prune34.0ms (0.2%)

simplify375.0ms (2.2%)

localize267.0ms (1.5%)

series29.0ms (0.2%)

simplify325.0ms (1.9%)

rewrite279.0ms (1.6%)

eval159.0ms (0.9%)

prune111.0ms (0.6%)

simplify333.0ms (1.9%)

localize387.0ms (2.2%)

series15.0ms (0.1%)

simplify451.0ms (2.6%)

rewrite269.0ms (1.6%)

eval110.0ms (0.6%)

prune100.0ms (0.6%)

simplify339.0ms (1.9%)

localize379.0ms (2.2%)

series26.0ms (0.2%)

simplify344.0ms (2%)

rewrite253.0ms (1.5%)

eval91.0ms (0.5%)

prune76.0ms (0.4%)

regimes45.0ms (0.3%)

regimes35.0ms (0.2%)

regimes32.0ms (0.2%)

regimes31.0ms (0.2%)

regimes29.0ms (0.2%)

regimes27.0ms (0.2%)

regimes23.0ms (0.1%)

regimes22.0ms (0.1%)

regimes20.0ms (0.1%)

regimes20.0ms (0.1%)

regimes9.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify12.0ms (0.1%)

soundness1.2s (7.1%)

preprocess119.0ms (0.7%)

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