Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze47.0ms (0.2%)

Memory

-4.4MiB live, 103.6MiB 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)

sample10.3s (54.5%)

Memory

-80.3MiB live, 11 731.4MiB allocated

Samples

4.0s	25 887×	0	invalid
3.4s	5 678×	2	valid
886.0ms	2 458×	1	valid
15.0ms	120×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.7s

ival-cos: 2.8s (42.3% of total)

const: 966.0ms (14.4% of total)

ival-<=: 592.0ms (8.8% of total)

ival-<: 488.0ms (7.3% of total)

adjust: 473.0ms (7% of total)

ival-mult: 386.0ms (5.7% of total)

ival-sub: 318.0ms (4.7% of total)

ival-add: 295.0ms (4.4% of total)

ival-fabs: 201.0ms (3% of total)

ival-and: 102.0ms (1.5% of total)

exact: 48.0ms (0.7% of total)

ival-assert: 14.0ms (0.2% of total)

Bogosity

explain227.0ms (1.2%)

Memory

1.0MiB live, 440.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
141	3	(6.453517206469507e-160 6.342938085853914e-164)	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	1	(304.4368816705219 0.09372853784433303)	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	144	1

Confusion

	Predicted +	Predicted -
+	141	1
-	3	111

Precision

0.9791666666666666

Recall

0.9929577464788732

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	141	1	0
-	3	0	111

Precision?

0.9793103448275862

Recall?

1.0

Freqs

test

number	freq
0	112
1	144

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

148.0ms	344×	2	valid
23.0ms	162×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-cos: 112.0ms (77.9% of total)

adjust: 18.0ms (12.5% of total)

ival-sub: 9.0ms (6.3% of total)

ival-add: 5.0ms (3.5% of total)

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

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

preprocess63.0ms (0.3%)

Memory

-28.3MiB live, 48.7MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

12.7MiB live, 12.7MiB 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)

localize102.0ms (0.5%)

Memory

10.7MiB live, 167.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.03304465476030194	(cos.f64 (+.f64 x eps))
accuracy	32.081901482300495	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

83.0ms	172×	2	valid
10.0ms	81×	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: 79.0ms

ival-cos: 55.0ms (69.6% of total)

adjust: 19.0ms (24% of total)

ival-sub: 3.0ms (3.8% of total)

ival-add: 2.0ms (2.5% of total)

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

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

series5.0ms (0%)

Memory

12.7MiB live, 12.7MiB 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	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	@	0	(cos (+ x eps))

simplify279.0ms (1.5%)

Memory

-29.2MiB live, 332.2MiB 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)

rewrite237.0ms (1.2%)

Memory

24.1MiB live, 305.6MiB 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 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (.f64 x x)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(neg.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (neg.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps))) (-.f64 x eps)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(/.f64 (*.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (*.f64 x x)))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (.f64 eps eps)) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps))) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)) (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))))
(.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (/.f64 (+.f64 x eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))))
(.f64 (.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 x)
(cos.f64 (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))

eval36.0ms (0.2%)

Memory: -14.6MiB live, 59.8MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune41.0ms (0.2%)

Memory

-6.5MiB live, 75.4MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

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

Accuracy

99.8%

Counts

307 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.9%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	49.9%	(/.f64 (-.f64 (.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))))) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	49.9%	(-.f64 (/.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))) (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))))) (cos.f64 x))
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	48.8%	(-.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))
▶	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Compiler

Compiled 395 to 240 computations (39.2% saved)

simplify296.0ms (1.6%)

Memory

17.0MiB live, 399.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(cos.f64 x)
cost-diff	6272	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
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

18 548×	`lower-fma.f32`
18 540×	`lower-fma.f64`
4 318×	`lower-*.f32`
4 304×	`lower-*.f64`
2 710×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	229
0	71	219
1	118	219
2	251	219
3	430	211
4	639	211
5	1196	211
6	3226	211
7	4514	211
8	7031	211
0	8275	206

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)
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(cos.f64 x)
x
(cos.f64 eps)
eps
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(sin.f64 x)
(sin.f64 eps)

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

localize388.0ms (2%)

Memory

-9.7MiB live, 522.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	0.00390625	(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
accuracy	32.091534699257366	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
accuracy	0.015625	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.03304465476030194	(cos.f64 (+.f64 x eps))
accuracy	0.7758644688725398	#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	32.081901482300495	(-.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	0.0078125	(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy	12.66504940365993	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(cos.f64 eps)
accuracy	31.780718216535718	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	32.168997283781714	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.015625	(.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	0.05581869791047188	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.1328125	(.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	0.24609375	(+.f64 x (+.f64 x eps))

Samples

301.0ms	177×	2	valid
41.0ms	78×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 204 to 40 computations (80.4% saved)

Precisions

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

ival-cos: 109.0ms (44.6% of total)

adjust: 66.0ms (27% of total)

ival-mult: 22.0ms (9% of total)

ival-add: 19.0ms (7.8% of total)

ival-sin: 16.0ms (6.5% of total)

ival-neg: 4.0ms (1.6% of total)

const: 4.0ms (1.6% of total)

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

exact: 1.0ms (0.4% of total)

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

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

series45.0ms (0.2%)

Memory

17.0MiB live, 94.2MiB allocated

Counts

22 → 432

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

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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin 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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (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 -1>
#<alt (- (* -1 (* x (sin eps))) 1)>
#<alt (- (* x (- (* 1/2 x) (sin eps))) 1)>
#<alt (- (* x (- (* x (+ 1/2 (* 1/6 (* x (sin eps))))) (sin eps))) 1)>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (cos x))>
#<alt (- (* -1 (* eps (sin x))) (cos x))>
#<alt (- (* eps (- (* 1/6 (* (pow eps 2) (sin x))) (sin x))) (cos x))>
#<alt (- (* eps (- (* (pow eps 2) (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))) (sin x))) (cos x))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (+ (cos x) (* (sin eps) (sin 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 (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt 1>
#<alt (+ 1 (* x (sin eps)))>
#<alt (+ 1 (* x (+ (sin eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2)))))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* eps (sin x)))>
#<alt (+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x))))))>
#<alt (+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x))))))))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>
#<alt (+ (cos x) (* (sin eps) (sin x)))>

Calls

108 calls:

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

simplify331.0ms (1.7%)

Memory

-15.1MiB live, 418.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 540×	`lower-fma.f64`
13 540×	`lower-fma.f32`
6 218×	`lower-*.f64`
6 218×	`lower-*.f32`
3 838×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	371	3677
1	1111	3520
2	2885	3473
3	6696	3473
0	8345	3227

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 407

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

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 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 x x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 x x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 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)))
(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 #s(literal 1/6 binary64) (.f64 eps eps) #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 (.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)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
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(- (* -1 (* eps (sin x))) (cos x))
(neg.f64 (fma.f64 eps (sin.f64 x) (cos.f64 x)))
(- (* eps (- (* 1/6 (* (pow eps 2) (sin x))) (sin x))) (cos x))
(-.f64 (.f64 eps (.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)))) (cos.f64 x))
(- (* eps (- (* (pow eps 2) (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))) (sin x))) (cos x))
(-.f64 (.f64 eps (-.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (sin.f64 x))) (cos.f64 x))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 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 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (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 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(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 (+ eps (* 2 x))))
(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 (- eps (* -2 x))))
(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 (- eps (* -2 x))))
(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 x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (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 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/8 binary64))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(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 (+ eps (* 2 x))))
(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))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
1
#s(literal 1 binary64)
(+ 1 (* x (sin eps)))
(fma.f64 x (sin.f64 eps) #s(literal 1 binary64))
(+ 1 (* x (+ (sin eps) (* -1/2 x))))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal 1 binary64))
(+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2)))))
(fma.f64 x (fma.f64 x (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)) (sin.f64 eps)) #s(literal 1 binary64))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(cos x)
(cos.f64 x)
(+ (cos x) (* eps (sin x)))
(fma.f64 eps (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x))))))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x))))))))
(fma.f64 eps (.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/120 binary64))))) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))

rewrite297.0ms (1.6%)

Memory

20.0MiB live, 409.6MiB allocated

Rules

4 372×	`lower-*.f32`
4 358×	`lower-*.f64`
4 160×	`lower-/.f64`
4 160×	`lower-/.f32`
2 960×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	173
0	71	161
1	254	161
2	2009	161
0	8448	156

Stop Event

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

Counts

22 → 576

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

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

eval128.0ms (0.7%)

Memory: 37.5MiB live, 224.8MiB allocated
Compiler: Compiled 30 070 to 2 767 computations (90.8% saved)

prune162.0ms (0.9%)

Memory

-63.8MiB live, 250.9MiB allocated

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	1 053	24	1 077
Fresh	3	2	5
Picked	3	2	5
Done	0	1	1
Total	1 059	29	1 088

Accuracy

100.0%

Counts

1 088 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	49.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	36.0%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.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 (/.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 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #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))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x (-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #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))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	35.5%	(.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))
	98.8%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.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))
	98.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.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))))) #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))
▶	48.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	24.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
	79.6%	#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)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	79.6%	#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))))))
	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
	80.6%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin x) (sin eps)) (cos x)))) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
	97.9%	#s(approx (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))

Compiler

Compiled 1 074 to 657 computations (38.8% saved)

simplify253.0ms (1.3%)

Memory

25.2MiB live, 301.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64))
cost-diff	1600	(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
cost-diff	0	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 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	0	(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
cost-diff	0	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
cost-diff	0	(.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

16 138×	`lower-fma.f32`
16 128×	`lower-fma.f64`
4 732×	`lower-*.f32`
4 704×	`lower-*.f64`
2 346×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	501
0	99	442
1	175	414
2	376	370
3	876	370
4	3588	370
5	7133	370
0	8379	360

Stop Event

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

Calls

Call 1

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

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(sin.f64 x)
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
x
(+.f64 x x)
x
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(cos.f64 x)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
(.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps))
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
x
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
(neg.f64 eps)
eps
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(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)
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 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 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #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 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #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 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(+.f64 eps (+.f64 x x))
(*.f64 (+.f64 x eps) (-.f64 x eps))
(*.f64 (+.f64 eps x) (-.f64 x eps))
(+.f64 x eps)
(+.f64 eps x)
x
(-.f64 x eps)
(/.f64 #s(literal 1 binary64) (-.f64 x eps))
#s(literal 1 binary64)
#s(literal -2 binary64)

localize497.0ms (2.6%)

Memory

-6.8MiB live, 279.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05581869791047188	(sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))
accuracy	0.12890625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64))))
accuracy	0.21875	(/.f64 #s(literal 1 binary64) (-.f64 x eps))
accuracy	22.362894061916013	(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.05581869791047188	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.12890625	(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy	0.24609375	(+.f64 x (+.f64 x eps))
accuracy	0.0859375	(.f64 x (.f64 x x))
accuracy	0.09375	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
accuracy	0.6618728787671687	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
accuracy	12.469531427903954	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
accuracy	0.236488567107694	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	31.541656640552652	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	31.92601721598528	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0.00390625	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01171875	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
accuracy	0.12890625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

255.0ms	176×	2	valid
64.0ms	76×	1	valid
12.0ms	3×	5	exit
1.0ms	1×	0	valid

Compiler

Compiled 444 to 59 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 261.0ms

ival-cos: 79.0ms (30.2% of total)

adjust: 65.0ms (24.9% of total)

ival-mult: 47.0ms (18% of total)

ival-sin: 24.0ms (9.2% of total)

ival-add: 21.0ms (8% of total)

const: 15.0ms (5.7% of total)

ival-div: 4.0ms (1.5% of total)

ival-sub: 4.0ms (1.5% 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)

series98.0ms (0.5%)

Memory

-6.9MiB live, 68.4MiB allocated

Counts

26 → 528

Calls

Call 1

Inputs
#<alt (*.f64 (+.f64 x x) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))>
#<alt (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))>
#<alt #s(approx (cos eps) #s(literal 1 binary64))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))>
#<alt (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps))>
#<alt #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))>
#<alt (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)>
#<alt (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))>
#<alt (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)>
#<alt (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))>
#<alt (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))>
#<alt (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))>
#<alt (.f64 x (.f64 x x))>
#<alt (+.f64 x (+.f64 x eps))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 x eps))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64))))>
#<alt (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))>

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1/2 (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 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 (* -1/5040 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<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 (* -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 (* 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 (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 (* 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 (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 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 (* 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 (* -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 (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/120 x)>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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 (/ -1 eps)>
#<alt (- (* -1 (/ x (pow eps 2))) (/ 1 eps))>
#<alt (- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (/ eps x)) x)>
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)>
#<alt (/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* -1 (/ eps x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (/ 1 x) (/ eps (pow x 2)))>
#<alt (+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))>
#<alt (+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ -1 eps)>
#<alt (/ (- (* -1 (/ x eps)) 1) eps)>
#<alt (/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)>
#<alt (/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)>
#<alt (/ -1 eps)>
#<alt (* -1 (/ (+ 1 (/ x eps)) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))>
#<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 (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

132 calls:

Time	Variable		Point	Expression
47.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
4.0ms	x	@	0	(* x (+ (* (* x x) -1/5040) 1/120))
2.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
2.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
2.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

simplify332.0ms (1.7%)

Memory

25.6MiB live, 215.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 244×	`lower-fma.f64`
11 244×	`lower-fma.f32`
5 930×	`lower-*.f64`
5 930×	`lower-*.f32`
4 384×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	453	5707
1	1387	5393
2	3903	5295
0	8318	4934

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 490

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
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)))
(/ -1 eps)
(- (* -1 (/ x (pow eps 2))) (/ 1 eps))
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(/ 1 x)
(/ (+ 1 (/ eps x)) x)
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)
(/ 1 x)
(* -1 (/ (- (* -1 (/ eps x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))
(/ 1 x)
(+ (/ 1 x) (/ eps (pow x 2)))
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ -1 eps)
(/ (- (* -1 (/ x eps)) 1) eps)
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)
(/ -1 eps)
(* -1 (/ (+ 1 (/ x eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))
(* 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 (* 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
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (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 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 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 (.f64 eps (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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
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(*.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)
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(- (* -1 (/ x (pow eps 2))) (/ 1 eps))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps)
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(fma.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) (/.f64 #s(literal -1 binary64) (.f64 eps eps))) (/.f64 #s(literal -1 binary64) eps))
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(fma.f64 x (.f64 x (-.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (/.f64 x (.f64 (.f64 eps eps) (.f64 eps eps))))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (/ eps x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x)
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)
(/.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) (-.f64 (/.f64 eps x) #s(literal -1 binary64)) (/.f64 eps x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* -1 (/ eps x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x)
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))
(/.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (/.f64 (*.f64 eps (fma.f64 eps (/.f64 eps x) eps)) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (/ 1 x) (/ eps (pow x 2)))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x)
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))
(fma.f64 eps (/.f64 eps (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 eps (fma.f64 eps (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) (/.f64 eps (.f64 x (*.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x))
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(/ (- (* -1 (/ x eps)) 1) eps)
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps)
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)) eps)
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)
(neg.f64 (/.f64 (+.f64 (fma.f64 (.f64 x x) (/.f64 x (.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)) eps))
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(* -1 (/ (+ 1 (/ x eps)) eps))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps)
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)) eps)
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (-.f64 (neg.f64 x) (/.f64 (*.f64 x (fma.f64 x (/.f64 x eps) x)) eps)) eps)) eps)
(* 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 (.f64 eps (sin.f64 x)) #s(literal -1/12 binary64) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 x (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (.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 (sin.f64 x) (.f64 eps #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))

rewrite479.0ms (2.5%)

Memory

-19.1MiB live, 341.4MiB allocated

Rules

5 684×	`lower-fma.f32`
5 674×	`lower-fma.f64`
4 136×	`lower-*.f32`
4 118×	`lower-*.f64`
4 044×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	383
0	99	352
1	340	204
2	2718	194
0	9357	194

Stop Event

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

Counts

26 → 1 168

Calls

Call 1

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

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

eval393.0ms (2.1%)

Memory: 27.5MiB live, 392.5MiB allocated
Compiler: Compiled 51 596 to 4 165 computations (91.9% saved)

prune204.0ms (1.1%)

Memory

13.6MiB live, 511.6MiB allocated

Pruning

35 alts after pruning (29 fresh and 6 done)

	Pruned	Kept	Total
New	1 791	14	1 805
Fresh	6	15	21
Picked	2	3	5
Done	0	3	3
Total	1 799	35	1 834

Accuracy

100.0%

Counts

1 834 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	49.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	22.3%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	36.0%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.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 (/.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 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	57.1%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (-.f64 x eps))) x) #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))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (+.f64 x eps) eps))))) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
▶	35.5%	(.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))
	98.8%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.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))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	80.2%	(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
✓	48.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	24.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
▶	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
	79.6%	#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)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	79.6%	#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))))))
▶	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
	80.6%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin x) (sin eps)) (cos x)))) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
	98.1%	#s(approx (* (* (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) -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)))))

Compiler

Compiled 1 613 to 837 computations (48.1% saved)

simplify399.0ms (2.1%)

Memory

-15.3MiB live, 442.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.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))))
cost-diff	0	(.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))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	1984	(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
cost-diff	0	(sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
cost-diff	0	(.f64 (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	832	(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
cost-diff	0	(sin.f64 x)
cost-diff	0	(.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
cost-diff	1024	(/.f64 (*.f64 eps eps) (neg.f64 eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 eps (neg.f64 x))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))

Rules

24 934×	`lower-fma.f32`
24 932×	`lower-fma.f64`
5 894×	`lower-*.f32`
5 864×	`lower-*.f64`
1 932×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	466
0	100	435
1	185	407
2	415	354
3	848	354
4	2087	354
5	3657	354
6	7542	354
0	8050	340

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

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

localize555.0ms (2.9%)

Memory

-7.6MiB live, 475.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
accuracy	0.12890625	(.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))))
accuracy	0.24609375	(+.f64 x (+.f64 x eps))
accuracy	40.51033626302626	(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
accuracy	0.0234375	(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
accuracy	0.05581869791047188	(sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
accuracy	0.12890625	(.f64 (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.28515625	(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
accuracy	0	(neg.f64 eps)
accuracy	0.0078125	(.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps)))
accuracy	12.469531427903954	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
accuracy	27.171657885179293	(/.f64 (*.f64 eps eps) (neg.f64 eps))
accuracy	0	(*.f64 eps (neg.f64 x))
accuracy	0	(neg.f64 x)
accuracy	1.1791891241538655	#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
accuracy	12.469531427903954	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
accuracy	0.00390625	(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01171875	(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.015625	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
accuracy	0.12890625	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

309.0ms	169×	2	valid
75.0ms	81×	1	valid
8.0ms	3×	5	exit
1.0ms	3×	0	valid

Compiler

Compiled 372 to 54 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 325.0ms

ival-cos: 120.0ms (37% of total)

adjust: 102.0ms (31.4% of total)

ival-mult: 60.0ms (18.5% of total)

ival-sin: 16.0ms (4.9% of total)

ival-add: 12.0ms (3.7% of total)

ival-div: 9.0ms (2.8% of total)

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

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

exact: 1.0ms (0.3% of total)

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

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

series132.0ms (0.7%)

Memory

-13.1MiB live, 107.0MiB allocated

Counts

26 → 540

Calls

Call 1

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

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

Calls

135 calls:

Time	Variable		Point	Expression
29.0ms	eps	@	-inf	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
27.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
22.0ms	x	@	inf	(* (sin x) (/ (* eps eps) (neg eps)))
5.0ms	eps	@	0	(* eps (+ 1/2 (/ x eps)))
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

simplify300.0ms (1.6%)

Memory

8.8MiB live, 525.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 784×	`lower-fma.f64`
16 784×	`lower-fma.f32`
6 056×	`lower-*.f64`
6 056×	`lower-*.f32`
3 508×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	5503
1	1003	5253
2	2743	5163
3	6214	5163
0	8361	4814

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 518

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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
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(+ (* 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 (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x 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)))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))

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

rewrite223.0ms (1.2%)

Memory

-2.0MiB live, 351.7MiB allocated

Rules

4 328×	`lower-fma.f32`
4 326×	`lower-fma.f64`
3 374×	`lower-/.f32`
3 368×	`lower-/.f64`
3 114×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	364
0	99	345
1	326	214
2	2577	205
0	8599	197

Stop Event

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

Counts

26 → 791

Calls

Call 1

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

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

eval178.0ms (0.9%)

Memory: 6.5MiB live, 356.7MiB allocated
Compiler: Compiled 34 142 to 3 474 computations (89.8% saved)

prune163.0ms (0.9%)

Memory

19.3MiB live, 342.0MiB allocated

Pruning

45 alts after pruning (38 fresh and 7 done)

	Pruned	Kept	Total
New	1 396	27	1 423
Fresh	13	11	24
Picked	3	2	5
Done	1	5	6
Total	1 413	45	1 458

Accuracy

100.0%

Counts

1 458 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	22.3%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	25.1%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) (neg.f64 x))))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	36.0%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.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 (/.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 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	57.1%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (-.f64 x eps))) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (+.f64 x eps) eps))))) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	98.8%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (.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))
✓	35.5%	(.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 (.f64 (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.8%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (.f64 eps eps)) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	53.5%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 x (.f64 eps eps)) eps #s(literal 1/2 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))) #s(literal -2 binary64))
	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal -2 binary64))
	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
✓	48.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	70.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
	24.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
	67.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
	68.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
	79.1%	#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
	79.6%	#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)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
	18.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
	69.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
	27.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
	80.6%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin x) (sin eps)) (cos x)))) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
	98.1%	#s(approx (* (* (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) -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)))))

Compiler

Compiled 2 519 to 914 computations (63.7% saved)

regimes56.0ms (0.3%)

Memory

1.8MiB live, 81.2MiB allocated

Counts

76 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#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 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 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))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64))))) (sin.f64 (.f64 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 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 x (.f64 eps eps)) eps #s(literal 1/2 binary64))))) (sin.f64 (*.f64 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 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.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 #s(literal 1 binary64) eps) (.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))
(.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 #s(approx (* (+ x (+ x eps)) 1/2) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (.f64 eps eps)) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.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))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #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))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x 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 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (-.f64 x eps))) x) #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 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) (neg.f64 x))))) #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 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin x) (sin eps)) (cos x)))) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
#s(approx (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) -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)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.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))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (+.f64 x eps) eps))))) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 (-.f64 (.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))))) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(-.f64 (/.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))) (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))))) (cos.f64 x))

Outputs

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

Calls

3 calls:

19.0ms	eps
18.0ms	x
14.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes50.0ms (0.3%)

Memory

-23.8MiB live, 54.1MiB allocated

Counts

68 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#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 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 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))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64))))) (sin.f64 (.f64 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 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (fma.f64 (/.f64 x (.f64 eps eps)) eps #s(literal 1/2 binary64))))) (sin.f64 (*.f64 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 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.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 #s(literal 1 binary64) eps) (.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))
(.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 #s(approx (* (+ x (+ x eps)) 1/2) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (.f64 eps eps)) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.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))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #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))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x 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 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (-.f64 x eps))) x) #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 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) (neg.f64 x))))) #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 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin x) (sin eps)) (cos x)))) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
#s(approx (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) -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)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.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))))) #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:

17.0ms	x
16.0ms	eps
13.0ms	(-.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

-22.1MiB live, 36.5MiB 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#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 (*.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin (* eps 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))

Calls

3 calls:

15.0ms	x
10.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.1%)

Memory

24.5MiB live, 24.5MiB allocated

Counts

36 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

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

regimes30.0ms (0.2%)

Memory

-14.8MiB live, 22.9MiB allocated

Counts

35 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)) (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))))) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

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

regimes28.0ms (0.1%)

Memory

-14.1MiB live, 23.7MiB 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) (neg.f64 x)))) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.1%)

Memory

34.0MiB live, 34.0MiB 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (-.f64 (-.f64 x eps) x))))
(-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (neg.f64 eps)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
80.2%	1	`x`
80.2%	1	`eps`
80.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

-2.3MiB live, 36.9MiB allocated

Counts

25 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (-.f64 (-.f64 x eps) x)))
(.f64 #s(approx ( (sin (* (+ x (+ x eps)) 1/2)) (sin (* eps 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) eps) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (*.f64 (/.f64 #s(literal -1 binary64) eps) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))

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

Calls

3 calls:

8.0ms	eps
7.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
80.2%	1	`x`
80.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
80.2%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-19.2MiB live, 25.8MiB allocated

Counts

16 → 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) (/.f64 (.f64 eps eps) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#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)))

Outputs

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

Calls

3 calls:

5.0ms	eps
5.0ms	x
4.0ms	(-.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)

regimes12.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

4.0ms	x
4.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.6%	1	`x`
79.6%	1	`eps`
79.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

6.7MiB live, 6.7MiB 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)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 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)) #s(approx (* (sin x) (/ (* eps eps) (neg eps))) (.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#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)) #s(approx (* (sin x) (neg eps)) (.f64 eps (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 x)) (.f64 eps eps))))

Outputs
#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)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.6%	1	`x`
79.6%	1	`eps`
79.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
#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))))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.6%	1	`x`
79.6%	1	`eps`
79.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

-35.1MiB 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)) #s(approx (+ (cos eps) -1) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.3%	1	`x`
79.3%	1	`eps`
79.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0%)

Memory

4.0MiB live, 4.0MiB 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	eps
1.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
48.6%	1	`x`
48.6%	1	`eps`
48.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Rules

92×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
18×	`neg-sub0_binary64`
18×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	406
1	177	406
2	204	406
3	224	406
4	234	406
5	237	406

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #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)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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)) #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)) #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) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #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)) (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 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))
#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))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#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 (neg.f64 eps) #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x))))
#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)) #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))))

soundness1.3s (7%)

Memory

-7.2MiB live, 32.3MiB allocated

Rules

16 784×	`lower-fma.f64`
16 784×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 540×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	364
0	99	345
1	326	214
2	2577	205
0	8599	197
0	453	5707
1	1387	5393
2	3903	5295
0	8318	4934
0	41	173
0	71	161
1	254	161
2	2009	161
0	8448	156
0	317	5503
1	1003	5253
2	2743	5163
3	6214	5163
0	8361	4814
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	371	3677
1	1111	3520
2	2885	3473
3	6696	3473
0	8345	3227
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
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 811 to 408 computations (49.7% saved)

preprocess82.0ms (0.4%)

Memory: -2.4MiB live, 75.7MiB allocated
Compiler: Compiled 562 to 218 computations (61.2% 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%)

analyze47.0ms (0.2%)

sample10.3s (54.5%)

explain227.0ms (1.2%)

preprocess63.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize102.0ms (0.5%)

series5.0ms (0%)

simplify279.0ms (1.5%)

rewrite237.0ms (1.2%)

eval36.0ms (0.2%)

prune41.0ms (0.2%)

simplify296.0ms (1.6%)

localize388.0ms (2%)

series45.0ms (0.2%)

simplify331.0ms (1.7%)

rewrite297.0ms (1.6%)

eval128.0ms (0.7%)

prune162.0ms (0.9%)

simplify253.0ms (1.3%)

localize497.0ms (2.6%)

series98.0ms (0.5%)

simplify332.0ms (1.7%)

rewrite479.0ms (2.5%)

eval393.0ms (2.1%)

prune204.0ms (1.1%)

simplify399.0ms (2.1%)

localize555.0ms (2.9%)

series132.0ms (0.7%)

simplify300.0ms (1.6%)

rewrite223.0ms (1.2%)

eval178.0ms (0.9%)

prune163.0ms (0.9%)

regimes56.0ms (0.3%)

regimes50.0ms (0.3%)

regimes35.0ms (0.2%)

regimes27.0ms (0.1%)

regimes30.0ms (0.2%)

regimes28.0ms (0.1%)

regimes23.0ms (0.1%)

regimes21.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0%)

regimes7.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify12.0ms (0.1%)

soundness1.3s (7%)

preprocess82.0ms (0.4%)

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