Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze43.0ms (0.2%)

Memory

-15.6MiB live, 60.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.9s (54.8%)

Memory

46.4MiB live, 11 552.3MiB allocated

Samples

4.0s	26 194×	0	invalid
3.5s	5 662×	2	valid
703.0ms	2 459×	1	valid
45.0ms	135×	0	valid

Precisions

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

ival-cos: 3.3s (48.8% of total)

const: 785.0ms (11.7% of total)

adjust: 460.0ms (6.8% of total)

ival-<: 421.0ms (6.3% of total)

ival-fabs: 370.0ms (5.5% of total)

ival-mult: 344.0ms (5.1% of total)

ival-<=: 314.0ms (4.7% of total)

ival-sub: 297.0ms (4.4% of total)

ival-add: 281.0ms (4.2% of total)

ival-and: 105.0ms (1.6% of total)

exact: 48.0ms (0.7% of total)

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

Bogosity

explain272.0ms (1.5%)

Memory

-16.5MiB live, 425.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
144	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
6	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
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
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	6	0

Confusion

	Predicted +	Predicted -
+	146	1
-	0	109

Precision

1.0

Recall

0.9931972789115646

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	1
-	0	0	109

Precision?

1.0

Recall?

0.9931972789115646

Freqs

test

number	freq
0	110
1	142
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

149.0ms	324×	2	valid
46.0ms	178×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 173.0ms

ival-cos: 142.0ms (82.3% of total)

adjust: 17.0ms (9.9% of total)

ival-add: 6.0ms (3.5% of total)

ival-sub: 6.0ms (3.5% of total)

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

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

preprocess28.0ms (0.2%)

Memory

24.4MiB live, 62.7MiB 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

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-23.4MiB live, 15.1MiB 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)

localize96.0ms (0.5%)

Memory

4.0MiB live, 149.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	32.54229867221464	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

72.0ms	162×	2	valid
11.0ms	89×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-cos: 56.0ms (80.4% of total)

adjust: 9.0ms (12.9% of total)

ival-sub: 4.0ms (5.7% of total)

ival-add: 2.0ms (2.9% of total)

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

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

series7.0ms (0%)

Memory

-26.2MiB live, 11.1MiB 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 (* -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 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 x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps 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 (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<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 (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 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 (- (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)>
#<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 eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps 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 (+ 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 x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (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 (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 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 (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify249.0ms (1.4%)

Memory

38.9MiB live, 386.6MiB 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	607	495
3	2403	494
4	7863	494
0	8013	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite338.0ms (1.9%)

Memory

-7.9MiB live, 497.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval38.0ms (0.2%)

Memory: 18.2MiB live, 92.3MiB allocated
Compiler: Compiled 8 023 to 877 computations (89.1% saved)

prune47.0ms (0.3%)

Memory

-5.2MiB live, 115.0MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	291	15	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	291	16	307

Accuracy

99.8%

Counts

307 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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))) #s(literal 2 binary64)) (.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)))))
	49.2%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #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 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))))
▶	48.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.1%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
▶	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
▶	99.5%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	47.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x))))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (- (cos (+ x eps)) (cos x)) (neg.f64 (*.f64 eps (sin.f64 x))))

Compiler

Compiled 597 to 358 computations (40% saved)

simplify222.0ms (1.2%)

Memory

-16.6MiB live, 250.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
cost-diff	448	(-.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)))
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
cost-diff	0	#s(approx (cos x) (fma.f64 x (*.f64 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 #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(+.f64 #s(literal -1 binary64) (cos.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
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

13 792×	`lower-fma.f32`
13 786×	`lower-fma.f64`
2 670×	`lower-*.f32`
2 656×	`lower-*.f64`
2 420×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	284
0	77	270
1	118	268
2	238	260
3	555	252
4	1285	252
5	3363	252
6	5744	252
0	8391	247

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

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

localize429.0ms (2.4%)

Memory

15.9MiB live, 396.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05435890382357724	(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.21051355301585636	(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	32.48427505454881	(-.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)))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	0.6591982251049965	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
accuracy	32.54229867221464	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	1.8725369591439622	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	32.54229867221464	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
accuracy	0	(cos.f64 eps)
accuracy	32.21940679149344	(+.f64 #s(literal -1 binary64) (cos.f64 eps))
accuracy	32.83146890767957	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.15234375	(.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	0.21158976492644632	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))

Samples

233.0ms	136×	2	valid
77.0ms	28×	3	valid
56.0ms	87×	1	valid
2.0ms	5×	0	valid

Compiler

Compiled 274 to 42 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 287.0ms

ival-cos: 176.0ms (61.4% of total)

adjust: 38.0ms (13.3% of total)

ival-mult: 22.0ms (7.7% of total)

ival-div: 20.0ms (7% of total)

ival-add: 17.0ms (5.9% of total)

ival-sub: 6.0ms (2.1% of total)

ival-sin: 6.0ms (2.1% of total)

exact: 1.0ms (0.3% of total)

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

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

series51.0ms (0.3%)

Memory

-29.6MiB live, 67.3MiB allocated

Counts

24 → 504

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

Outputs
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 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 (* 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 (* -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 (* -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 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 (* -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 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 x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps 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 (/ -1 (* eps (sin x)))>
#<alt (/ (- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) eps)>
#<alt (/ (- (* eps (- (* -1 (* eps (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)>
#<alt (/ (- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))) (* 1/6 (/ 1 (sin x))))) (sin x))) (+ (* -1/12 (/ (cos x) (pow (sin x) 2))) (* 1/24 (/ (cos x) (pow (sin x) 2))))))) (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)>
#<alt (* -1 (* eps (sin x)))>
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#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (* -1 (* eps (sin (* 2 x))))>
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#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))>
#<alt (* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (/ 1/2 (cos x))>
#<alt (+ (* 1/4 (/ (* eps (sin x)) (pow (cos x) 2))) (* 1/2 (/ 1 (cos x))))>
#<alt (+ (* eps (- (* eps (- (* 1/8 (/ 1 (cos x))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/4 (/ (sin x) (pow (cos x) 2))))) (* 1/2 (/ 1 (cos x))))>
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/8 (/ 1 (cos x))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/16 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/8 (/ 1 (cos x)))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/4 (/ (sin x) (pow (cos x) 2))))) (* 1/2 (/ 1 (cos x))))>
#<alt (* 2 (cos x))>
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#<alt (+ (* 2 (cos x)) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (* 2 (cos x)) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (* 2 x)>
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#<alt (+ eps (* 2 x))>
#<alt (sin x)>
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#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (cos (* 2 x))>
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#<alt (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))>
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#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))>
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#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
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#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
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#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 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 eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
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#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
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#<alt (* eps (+ 1 (/ x eps)))>
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#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (- (cos (+ eps x)) (cos x))>
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#<alt (+ (cos x) (cos (+ eps x)))>
#<alt (+ (cos x) (cos (+ eps x)))>
#<alt eps>
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#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (* 1/2 eps)>
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#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
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#<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 (* (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 (- (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) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<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))>
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#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
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#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ 1 (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ 1 (+ (cos x) (cos (- x (* -1 eps)))))>
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#<alt (+ (cos x) (cos (- x (* -1 eps))))>
#<alt (+ (cos x) (cos (- x (* -1 eps))))>
#<alt eps>
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#<alt (+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))>
#<alt (* 1/2 eps)>
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#<alt (+ x (* 1/2 eps))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
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#<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 (pow (sin (* 1/2 eps)) 2)>
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#<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 (- (cos eps) 1)>
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#<alt (- (cos eps) 1)>
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#<alt (cos eps)>
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#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt 1>
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#<alt (/ 1 (- (cos eps) 1))>
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#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* 1/6 (/ (sin eps) (pow (- (cos eps) 1) 2))) (+ (/ (* (sin eps) (+ 1/2 (* -1/2 (cos eps)))) (pow (- (cos eps) 1) 3)) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 2) (pow (- (cos eps) 1) 3))) (+ (* -1/2 (/ (cos eps) (pow (- (cos eps) 1) 2))) (* 1/2 (/ 1 (pow (- (cos eps) 1) 2)))))) (- (cos eps) 1)))))) (+ (* -1 (/ (pow (sin eps) 2) (pow (- (cos eps) 1) 3))) (+ (* -1/2 (/ (cos eps) (pow (- (cos eps) 1) 2))) (* 1/2 (/ 1 (pow (- (cos eps) 1) 2))))))) (* -1 (/ (sin eps) (pow (- (cos eps) 1) 2))))) (/ 1 (- (cos eps) 1)))>
#<alt (- (cos eps) 1)>
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#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
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#<alt (- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)>
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#<alt (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (+ 1 (cos eps)))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (+ (* x (- (* 2/3 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))) (/ (* (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))) (- (* -1/2 (cos eps)) 1/2)) (+ 1 (cos eps))))))) (/ 1 (+ 1 (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (/ 1 (+ 1 (cos eps)))>
#<alt (+ (/ 1 (+ 1 (cos eps))) (/ (* x (sin eps)) (pow (+ 1 (cos eps)) 2)))>
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (sin eps) (pow (+ 1 (cos eps)) 2))))) (/ 1 (+ 1 (cos eps))))>
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (sin eps) (pow (+ 1 (cos eps)) 2))) (/ (* (sin eps) (- (* -1/2 (cos eps)) 1/2)) (pow (+ 1 (cos eps)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2)))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (sin eps) (pow (+ 1 (cos eps)) 2))))) (/ 1 (+ 1 (cos eps))))>
#<alt (+ 1 (cos eps))>
#<alt (+ 1 (+ (cos eps) (* -1 (* x (sin eps)))))>
#<alt (+ 1 (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) 1/2)) (sin eps)))))>
#<alt (+ 1 (+ (cos eps) (* x (- (* x (- (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))) 1/2)) (sin eps)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ 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 (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (cos (* 2 eps))>
#<alt (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 eps))))>
#<alt (+ 1/2 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps))))))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 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 (* -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)) (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 x)) (cos 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 (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos 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 (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (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 x)) (cos x))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ 1 (+ (cos x) (cos (+ eps x))))>
#<alt (/ 1 (+ (cos x) (cos (+ eps x))))>
#<alt (/ 1 (+ (cos x) (cos (+ eps x))))>
#<alt (/ 1 (+ (cos x) (cos (+ eps x))))>
#<alt (+ (cos x) (cos (+ eps x)))>
#<alt (+ (cos x) (cos (+ eps x)))>
#<alt (+ (cos x) (cos (+ eps x)))>
#<alt (+ (cos x) (cos (+ eps x)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps 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 (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 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 (* -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)) (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 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 (- (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)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 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 (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (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 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (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 (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ 1 (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ 1 (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ 1 (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ 1 (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (+ (cos x) (cos (- eps (* -1 x))))>
#<alt (+ (cos x) (cos (- eps (* -1 x))))>
#<alt (+ (cos x) (cos (- eps (* -1 x))))>
#<alt (+ (cos x) (cos (- eps (* -1 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 (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 (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	x	@	-inf	((* (+ x (+ x eps)) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (/ 1 (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (sin (* (+ eps 0) 1/2)) (* x -1/2) (cos (* (+ x eps) 2)) (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2))
9.0ms	eps	@	inf	((* (+ x (+ x eps)) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (/ 1 (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (sin (* (+ eps 0) 1/2)) (* x -1/2) (cos (* (+ x eps) 2)) (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2))
8.0ms	x	@	0	((* (+ x (+ x eps)) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (/ 1 (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (sin (* (+ eps 0) 1/2)) (* x -1/2) (cos (* (+ x eps) 2)) (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2))
5.0ms	eps	@	0	((* (+ x (+ x eps)) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (/ 1 (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (sin (* (+ eps 0) 1/2)) (* x -1/2) (cos (* (+ x eps) 2)) (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2))
4.0ms	x	@	inf	((* (+ x (+ x eps)) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (/ 1 (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (sin (* (+ eps 0) 1/2)) (* x -1/2) (cos (* (+ x eps) 2)) (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2))

simplify241.0ms (1.3%)

Memory

19.1MiB live, 398.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 868×	`lower-fma.f64`
8 868×	`lower-fma.f32`
6 342×	`lower-*.f64`
6 342×	`lower-*.f32`
2 964×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	673	6162
1	2040	5951
2	5819	5912
0	8072	5589

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 480

Calls

Call 1

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

Outputs
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)
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.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 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.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))))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* 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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* 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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 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))))
(fma.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* 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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(/ -1 (* eps (sin x)))
(/.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))
(/ (- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) eps)
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))
(/ (- (* eps (- (* -1 (* eps (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)
(fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
(/ (- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))) (* 1/6 (/ 1 (sin x))))) (sin x))) (+ (* -1/12 (/ (cos x) (pow (sin x) 2))) (* 1/24 (/ (cos x) (pow (sin x) 2))))))) (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)
(fma.f64 (fma.f64 eps (neg.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* 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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* -1 (* eps (sin (* 2 x))))
(.f64 eps (sin.f64 (.f64 x #s(literal -2 binary64))))
(* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))
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(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (neg.f64 (-.f64 #s(literal -2 binary64) (/.f64 eps x))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (neg.f64 (-.f64 #s(literal -2 binary64) (/.f64 eps x))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (neg.f64 (-.f64 #s(literal -2 binary64) (/.f64 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))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps)))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x eps))) #s(literal 1/2 binary64))

rewrite223.0ms (1.2%)

Memory

-3.8MiB live, 193.7MiB allocated

Rules

1 110×	`lower-fma.f32`
1 104×	`lower-fma.f64`
1 070×	`lower-*.f32`
1 058×	`lower-*.f64`
904×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	214
0	77	206
1	286	149
0	2357	148

Stop Event

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

Counts

24 → 624

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

Outputs
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(+.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 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 eps) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 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) eps #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x eps) eps (.f64 x x))))
(/.f64 (.f64 eps (-.f64 #s(literal 0 binary64) eps)) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 eps) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps)) (fma.f64 (+.f64 x eps) eps (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (-.f64 #s(literal 0 binary64) eps))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(/.f64 (.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) #s(literal 1/2 binary64)) (fma.f64 (+.f64 x eps) eps (.f64 x x)))
(/.f64 (.f64 (.f64 eps (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x 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))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x))
(fma.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(fma.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) (.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 eps (-.f64 #s(literal 0 binary64) eps))))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) eps (*.f64 x x)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 eps eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps)) (neg.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 x (+.f64 x eps)))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps)
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (.f64 x x))))
(.f64 (.f64 eps (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(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 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
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eval186.0ms (1%)

Memory: 30.7MiB live, 306.8MiB allocated
Compiler: Compiled 33 999 to 2 694 computations (92.1% saved)

prune188.0ms (1%)

Memory

-3.6MiB live, 343.2MiB allocated

Pruning

39 alts after pruning (37 fresh and 2 done)

	Pruned	Kept	Total
New	1 322	30	1 352
Fresh	3	7	10
Picked	4	1	5
Done	0	1	1
Total	1 329	39	1 368

Accuracy

100.0%

Counts

1 368 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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))) #s(literal 2 binary64)) (.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)))))
	49.2%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #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 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
	97.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))))
	47.5%	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
	52.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (fma.f64 eps (neg.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))))
	59.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.0%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	98.5%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 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))
	99.5%	(.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))
	44.3%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (.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)))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.5%	(.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 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.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))
	42.4%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (.f64 x x)))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	39.1%	(.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))
▶	98.3%	(.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))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
	47.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x))))
	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 1 851 to 1 111 computations (40% saved)

simplify219.0ms (1.2%)

Memory

-27.3MiB live, 310.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	128	(*.f64 x #s(literal 2 binary64))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
cost-diff	0	(.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))))
cost-diff	0	(.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))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	1344	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.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	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))

Rules

12 280×	`lower-fma.f32`
12 270×	`lower-fma.f64`
3 882×	`lower-*.f32`
3 848×	`lower-*.f64`
2 374×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	546
0	118	503
1	213	491
2	540	483
3	1462	462
4	3283	462
5	5763	462
0	8120	460

Stop Event

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

Calls

Call 1

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

localize529.0ms (2.9%)

Memory

35.4MiB live, 821.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03582001953688403	(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
accuracy	0.140625	(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	0.7234893308688336	#s(approx (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64))))))
accuracy	0.15234375	(.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))))
accuracy	0.21158976492644635	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))
accuracy	26.913293192209373	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.11564352653852594	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.15234375	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.21158976492644635	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))
accuracy	0.6901122721602273	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	32.21940679149344	(+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64)))
accuracy	32.83146890767957	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.15234375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.21158976492644632	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

314.0ms	162×	2	valid
111.0ms	86×	1	valid
14.0ms	3×	3	valid
3.0ms	5×	0	valid

Compiler

Compiled 445 to 68 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 338.0ms

ival-cos: 136.0ms (40.3% of total)

ival-mult: 59.0ms (17.5% of total)

adjust: 58.0ms (17.2% of total)

ival-add: 29.0ms (8.6% of total)

ival-sin: 23.0ms (6.8% of total)

const: 15.0ms (4.4% of total)

ival-sub: 9.0ms (2.7% of total)

ival-div: 7.0ms (2.1% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

series56.0ms (0.3%)

Memory

-16.1MiB live, 27.3MiB allocated

Counts

25 → 528

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
36.0ms	x	@	-inf	((* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) (sin (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* eps eps) (/ 1 eps)) (* (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (* x 2) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (sin (+ (* 1/2 eps) x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (cos (+ x eps)) (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2))))
3.0ms	eps	@	-inf	((* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) (sin (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* eps eps) (/ 1 eps)) (* (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (* x 2) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (sin (+ (* 1/2 eps) x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (cos (+ x eps)) (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2))))
3.0ms	eps	@	inf	((* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) (sin (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* eps eps) (/ 1 eps)) (* (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (* x 2) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (sin (+ (* 1/2 eps) x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (cos (+ x eps)) (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2))))
3.0ms	x	@	inf	((* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) (sin (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* eps eps) (/ 1 eps)) (* (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (* x 2) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (sin (+ (* 1/2 eps) x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (cos (+ x eps)) (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2))))
2.0ms	eps	@	0	((* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) (sin (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (cos eps) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* eps eps) (/ 1 eps)) (* (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))) (* x 2) (/ 1 (+ (cos (+ x eps)) (cos x))) (+ (cos (+ x eps)) (cos x)) (sin (+ (* 1/2 eps) x)) (+ x (+ x eps)) (sin (* (+ x (+ x eps)) 1/2)) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (cos (+ x eps)) (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2))))

simplify255.0ms (1.4%)

Memory

20.5MiB live, 260.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 068×	`lower-fma.f64`
7 068×	`lower-fma.f32`
6 624×	`lower-*.f64`
6 624×	`lower-*.f32`
2 330×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	576	7019
1	1740	6651
2	4717	6617
0	8162	6218

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 510

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

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 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 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 (.f64 eps (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))))
(* 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 (.f64 eps (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))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* 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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 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 (.f64 eps (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))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 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 (.f64 eps (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))))
(* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))
(/.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 (*.f64 x #s(literal 2 binary64)))) (cos.f64 x))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 x #s(literal 2 binary64)))) (cos.f64 x))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal -1/8 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 x #s(literal 2 binary64)))) (cos.f64 x))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (fma.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal -1/8 binary64))))) (cos.f64 x)) (fma.f64 (sin.f64 x) (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/24 binary64)) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/4 binary64))))) (fma.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) #s(literal -1/8 binary64))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 x)) (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/4 binary64)) (sin.f64 (.f64 x #s(literal -2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 x #s(literal 2 binary64)))) (cos.f64 x))))
(/ 1/2 (cos x))
(/.f64 #s(literal 1/2 binary64) (cos.f64 x))
(+ (* 1/4 (/ (* eps (sin x)) (pow (cos x) 2))) (* 1/2 (/ 1 (cos x))))
(fma.f64 eps (/.f64 (*.f64 (sin.f64 x) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(+ (* eps (- (* eps (- (* 1/8 (/ 1 (cos x))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/4 (/ (sin x) (pow (cos x) 2))))) (* 1/2 (/ 1 (cos x))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (cos.f64 x))) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x)))
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x
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(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* (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) (* -1 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) (* -1 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) (* -1 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) (* -1 x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) 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))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* (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)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(+ (cos x) (cos (- eps (* -1 x))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 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)))
(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))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
(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))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (.f64 x #s(literal -2 binary64))))

rewrite217.0ms (1.2%)

Memory

-0.7MiB live, 119.4MiB allocated

Rules

2 086×	`lower-fma.f32`
2 076×	`lower-fma.f64`
1 798×	`lower-*.f32`
1 766×	`lower-*.f64`
1 264×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	382
0	118	346
1	432	286
0	3627	286

Stop Event

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

Counts

25 → 369

Calls

Call 1

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

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

eval242.0ms (1.3%)

Memory: -16.4MiB live, 177.4MiB allocated
Compiler: Compiled 26 225 to 2 028 computations (92.3% saved)

prune178.0ms (1%)

Memory

22.1MiB live, 182.2MiB allocated

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	1 032	13	1 045
Fresh	16	16	32
Picked	4	1	5
Done	0	2	2
Total	1 052	32	1 084

Accuracy

100.0%

Counts

1 084 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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))) #s(literal 2 binary64)) (.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)))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
▶	47.5%	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.0%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (fma.f64 eps (.f64 x #s(literal -2 binary64)) (.f64 eps (neg.f64 eps))))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	97.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 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 (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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))
	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.2%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	98.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	76.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
	47.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x))))
▶	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 1 284 to 782 computations (39.1% saved)

simplify539.0ms (3%)

Memory

-9.4MiB live, 486.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	192	(*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
cost-diff	12224	(exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64)))
cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
cost-diff	0	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
cost-diff	0	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
cost-diff	0	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (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	0	(*.f64 eps #s(literal -1/2 binary64))
cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (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 eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.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 eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	7168	(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))

Rules

36 774×	`lower-fma.f64`
36 774×	`lower-fma.f32`
3 838×	`lower-*.f32`
3 808×	`lower-*.f64`
2 546×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	406
0	88	369
1	137	368
2	257	368
3	411	356
4	537	356
5	735	356
6	1295	356
7	3671	356
8	6105	356
0	8116	346

Stop Event

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

Calls

Call 1

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

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

localize419.0ms (2.3%)

Memory

-23.0MiB live, 588.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2295982161796743	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
accuracy	1.4519214917146628	(exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64)))
accuracy	14.435425226681616	(log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
accuracy	15.256112936059601	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
accuracy	0.01171875	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy	0.015625	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy	0.0703125	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
accuracy	0.33100744294892115	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
accuracy	0.078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.1171875	(+.f64 x (+.f64 x eps))
accuracy	0.11969751705406045	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.31395844320434124	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
accuracy	0	(*.f64 eps #s(literal -1/2 binary64))
accuracy	0.3223031793629511	#s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
accuracy	16.05015768892118	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.0078125	(.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0625	(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))

Samples

127.0ms	83×	2	valid
68.0ms	43×	2	invalid
49.0ms	75×	1	invalid
28.0ms	40×	1	valid
11.0ms	2×	3	valid
3.0ms	11×	0	invalid
1.0ms	2×	0	valid

Compiler

Compiled 315 to 45 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-cos: 103.0ms (42.7% of total)

ival-mult: 45.0ms (18.6% of total)

adjust: 28.0ms (11.6% of total)

ival-sin: 14.0ms (5.8% of total)

ival-sub: 13.0ms (5.4% of total)

ival-log: 12.0ms (5% of total)

ival-add: 11.0ms (4.6% of total)

ival-div: 8.0ms (3.3% of total)

ival-exp: 7.0ms (2.9% of total)

exact: 1.0ms (0.4% of total)

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

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

series157.0ms (0.9%)

Memory

9.0MiB live, 286.4MiB allocated

Counts

25 → 552

Calls

Call 1

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

Outputs
#<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 (* -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 (* 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 (* 1/4 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/4 (cos x))))>
#<alt (* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/1440 (* (pow eps 2) (cos x)))))))>
#<alt (* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/80640 (* (pow eps 2) (cos x))) (* 1/1440 (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 (* -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 (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 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 (* 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 (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* -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 (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (/ -1 (* eps (sin x)))>
#<alt (/ (- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) eps)>
#<alt (/ (- (* eps (- (* -1 (* eps (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)>
#<alt (/ (- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))) (* 1/6 (/ 1 (sin x))))) (sin x))) (+ (* -1/12 (/ (cos x) (pow (sin x) 2))) (* 1/24 (/ (cos x) (pow (sin x) 2))))))) (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)>
#<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 (* -1 (+ (log eps) (log (neg (sin x)))))>
#<alt (+ (* -1 (+ (log eps) (log (neg (sin x))))) (* -1/2 (/ (* eps (cos x)) (sin x))))>
#<alt (+ (* -1 (+ (log eps) (log (neg (sin x))))) (* eps (+ (* -1/2 (* eps (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))) (* -1/2 (/ (cos x) (sin x))))))>
#<alt (+ (* -1 (+ (log eps) (log (neg (sin x))))) (* eps (+ (* -1/2 (/ (cos x) (sin x))) (* eps (+ (* -1/2 (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3)) (* -1/6 (* eps (+ (* -1/4 (/ (cos x) (sin x))) (+ (* 1/4 (/ (pow (cos x) 3) (pow (sin x) 3))) (* 1/2 (/ (cos x) (sin x))))))))))))>
#<alt (+ (log eps) (log (neg (sin x))))>
#<alt (+ (log eps) (+ (log (neg (sin x))) (* 1/2 (/ (* eps (cos x)) (sin x)))))>
#<alt (+ (log eps) (+ (log (neg (sin x))) (* eps (+ (* 1/2 (* eps (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))) (* 1/2 (/ (cos x) (sin x)))))))>
#<alt (+ (log eps) (+ (log (neg (sin x))) (* eps (+ (* 1/2 (/ (cos x) (sin x))) (* eps (+ (* 1/6 (* eps (+ (* -1/4 (/ (cos x) (sin x))) (+ (* 1/4 (/ (pow (cos x) 3) (pow (sin x) 3))) (* 1/2 (/ (cos x) (sin x))))))) (* 1/2 (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))))))))>
#<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 (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x))))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (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 (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 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 x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<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)) (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 x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<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)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -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 (* -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)) (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))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<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 (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (cos (+ eps x)) (cos x)))>
#<alt (/ 1 (- (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 x)) (cos x))>
#<alt (* -1 (log (- (cos (+ eps x)) (cos x))))>
#<alt (* -1 (log (- (cos (+ eps x)) (cos x))))>
#<alt (* -1 (log (- (cos (+ eps x)) (cos x))))>
#<alt (* -1 (log (- (cos (+ eps x)) (cos x))))>
#<alt (log (- (cos (+ eps x)) (cos x)))>
#<alt (log (- (cos (+ eps x)) (cos x)))>
#<alt (log (- (cos (+ eps x)) (cos x)))>
#<alt (log (- (cos (+ eps x)) (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 (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 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 eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<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) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 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 (* (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)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
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#<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)) (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 x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (cos x) (pow (sin (* 1/2 eps)) 2))>
#<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 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 (* -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)) (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 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 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (/ 1 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (/ 1 (- (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 (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (log (- (cos (- eps (* -1 x))) (cos x))))>
#<alt (* -1 (log (- (cos (- eps (* -1 x))) (cos x))))>
#<alt (* -1 (log (- (cos (- eps (* -1 x))) (cos x))))>
#<alt (* -1 (log (- (cos (- eps (* -1 x))) (cos x))))>
#<alt (log (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (log (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (log (- (cos (- eps (* -1 x))) (cos x)))>
#<alt (log (- (cos (- eps (* -1 x))) (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 (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 eps)) (* (sin x) (sin (* 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 (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<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))>

Calls

6 calls:

Time	Variable		Point	Expression
43.0ms	x	@	inf	((+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (* eps (* eps -1/2)) (* eps -1/2) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (- (* eps (* -1/2 (cos x))) (sin x)) (* eps (* -1/2 (cos x))) (exp (* (log (- (cos (+ x eps)) (cos x))) -1)) (/ 1 (exp (* (log (- (cos (+ x eps)) (cos x))) -1))) (* (log (- (cos (+ x eps)) (cos x))) -1) (log (- (cos (+ x eps)) (cos x))) (* (sin (* eps 1/2)) (cos x)) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))) (sin (* (+ x (+ x eps)) 1/2)) (+ x (+ x eps)) (- (cos (+ x eps)) (cos x)))
41.0ms	eps	@	inf	((+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (* eps (* eps -1/2)) (* eps -1/2) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (- (* eps (* -1/2 (cos x))) (sin x)) (* eps (* -1/2 (cos x))) (exp (* (log (- (cos (+ x eps)) (cos x))) -1)) (/ 1 (exp (* (log (- (cos (+ x eps)) (cos x))) -1))) (* (log (- (cos (+ x eps)) (cos x))) -1) (log (- (cos (+ x eps)) (cos x))) (* (sin (* eps 1/2)) (cos x)) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))) (sin (* (+ x (+ x eps)) 1/2)) (+ x (+ x eps)) (- (cos (+ x eps)) (cos x)))
28.0ms	x	@	-inf	((+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (* eps (* eps -1/2)) (* eps -1/2) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (- (* eps (* -1/2 (cos x))) (sin x)) (* eps (* -1/2 (cos x))) (exp (* (log (- (cos (+ x eps)) (cos x))) -1)) (/ 1 (exp (* (log (- (cos (+ x eps)) (cos x))) -1))) (* (log (- (cos (+ x eps)) (cos x))) -1) (log (- (cos (+ x eps)) (cos x))) (* (sin (* eps 1/2)) (cos x)) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))) (sin (* (+ x (+ x eps)) 1/2)) (+ x (+ x eps)) (- (cos (+ x eps)) (cos x)))
21.0ms	eps	@	-inf	((+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (* eps (* eps -1/2)) (* eps -1/2) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (- (* eps (* -1/2 (cos x))) (sin x)) (* eps (* -1/2 (cos x))) (exp (* (log (- (cos (+ x eps)) (cos x))) -1)) (/ 1 (exp (* (log (- (cos (+ x eps)) (cos x))) -1))) (* (log (- (cos (+ x eps)) (cos x))) -1) (log (- (cos (+ x eps)) (cos x))) (* (sin (* eps 1/2)) (cos x)) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))) (sin (* (+ x (+ x eps)) 1/2)) (+ x (+ x eps)) (- (cos (+ x eps)) (cos x)))
12.0ms	eps	@	0	((+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (- (cos (+ x eps)) (cos x)) (+ -1 (cos eps)) (* eps (* eps -1/2)) (* eps -1/2) (* (+ x (+ x eps)) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2) (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (sin (* (+ eps 0) 1/2)) (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (- (* eps (* -1/2 (cos x))) (sin x)) (* eps (* -1/2 (cos x))) (exp (* (log (- (cos (+ x eps)) (cos x))) -1)) (/ 1 (exp (* (log (- (cos (+ x eps)) (cos x))) -1))) (* (log (- (cos (+ x eps)) (cos x))) -1) (log (- (cos (+ x eps)) (cos x))) (* (sin (* eps 1/2)) (cos x)) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))) (sin (* (+ x (+ x eps)) 1/2)) (+ x (+ x eps)) (- (cos (+ x eps)) (cos x)))

simplify296.0ms (1.6%)

Memory

4.7MiB live, 544.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 028×	`lower-fma.f64`
12 028×	`lower-fma.f32`
8 046×	`lower-*.f64`
8 046×	`lower-*.f32`
3 368×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	606	6865
1	1971	6483
2	6230	6440
0	8638	6104

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 546

Calls

Call 1

Inputs
(* 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))))))))))
(* -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)))))))))
(* 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))))))))))
(* 1/4 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/4 (cos x))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/1440 (* (pow eps 2) (cos x)))))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/80640 (* (pow eps 2) (cos x))) (* 1/1440 (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)))
(* -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))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 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)))))))))
(* 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))))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -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)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(/ -1 (* eps (sin x)))
(/ (- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) eps)
(/ (- (* eps (- (* -1 (* eps (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)
(/ (- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))) (* 1/6 (/ 1 (sin x))))) (sin x))) (+ (* -1/12 (/ (cos x) (pow (sin x) 2))) (* 1/24 (/ (cos x) (pow (sin x) 2))))))) (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)
(* -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)))
(* -1 (+ (log eps) (log (neg (sin x)))))
(+ (* -1 (+ (log eps) (log (neg (sin x))))) (* -1/2 (/ (* eps (cos x)) (sin x))))
(+ (* -1 (+ (log eps) (log (neg (sin x))))) (* eps (+ (* -1/2 (* eps (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))) (* -1/2 (/ (cos x) (sin x))))))
(+ (* -1 (+ (log eps) (log (neg (sin x))))) (* eps (+ (* -1/2 (/ (cos x) (sin x))) (* eps (+ (* -1/2 (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3)) (* -1/6 (* eps (+ (* -1/4 (/ (cos x) (sin x))) (+ (* 1/4 (/ (pow (cos x) 3) (pow (sin x) 3))) (* 1/2 (/ (cos x) (sin x))))))))))))
(+ (log eps) (log (neg (sin x))))
(+ (log eps) (+ (log (neg (sin x))) (* 1/2 (/ (* eps (cos x)) (sin x)))))
(+ (log eps) (+ (log (neg (sin x))) (* eps (+ (* 1/2 (* eps (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))) (* 1/2 (/ (cos x) (sin x)))))))
(+ (log eps) (+ (log (neg (sin x))) (* eps (+ (* 1/2 (/ (cos x) (sin x))) (* eps (+ (* 1/6 (* eps (+ (* -1/4 (/ (cos x) (sin x))) (+ (* 1/4 (/ (pow (cos x) 3) (pow (sin x) 3))) (* 1/2 (/ (cos x) (sin x))))))) (* 1/2 (- (* -1/4 (/ (pow (cos x) 2) (pow (sin x) 2))) 1/3))))))))
(* 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))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x))))))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (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))))))))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 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 x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -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))))))
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(* -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)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(/ 1 (- (cos (+ eps x)) (cos x)))
(/ 1 (- (cos (+ eps x)) (cos x)))
(/ 1 (- (cos (+ eps x)) (cos x)))
(/ 1 (- (cos (+ eps x)) (cos x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (log (- (cos (+ eps x)) (cos x))))
(* -1 (log (- (cos (+ eps x)) (cos x))))
(* -1 (log (- (cos (+ eps x)) (cos x))))
(* -1 (log (- (cos (+ eps x)) (cos x))))
(log (- (cos (+ eps x)) (cos x)))
(log (- (cos (+ eps x)) (cos x)))
(log (- (cos (+ eps x)) (cos x)))
(log (- (cos (+ eps x)) (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 (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 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))))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -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))))))
(* (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 x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -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))))))
(* (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 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/ 1 (- (cos (- eps (* -1 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 (log (- (cos (- eps (* -1 x))) (cos x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log (- (cos (- eps (* -1 x))) (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 (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 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))))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))

Outputs
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 #s(literal 1/4 binary64) (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -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 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 #s(literal 1/4 binary64) (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -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 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* 1/4 (* (pow eps 2) (cos x)))
(.f64 (.f64 eps (cos.f64 x)) (*.f64 eps #s(literal 1/4 binary64)))
(* (pow eps 2) (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/4 (cos x))))
(.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/1440 (* (pow eps 2) (cos x)))))))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/1440 binary64) (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 #s(literal 1/4 binary64) (cos.f64 x))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/80640 (* (pow eps 2) (cos x))) (* 1/1440 (cos x))))))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/80640 binary64) (.f64 eps eps) #s(literal 1/1440 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
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 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #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 (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 #s(literal 1/4 binary64) (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -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 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(/ -1 (* eps (sin x)))
(/.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))
(/ (- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) eps)
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))
(/ (- (* eps (- (* -1 (* eps (+ (* 1/6 (/ 1 (sin x))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3)))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) eps)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))
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(log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.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))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(- (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) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(.f64 (cos.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (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))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(- (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))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ 1 (- (cos (- eps (* -1 x))) (cos x)))
(/.f64 #s(literal 1 binary64) (-.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 (log (- (cos (- eps (* -1 x))) (cos x))))
(neg.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(neg.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(neg.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(* -1 (log (- (cos (- eps (* -1 x))) (cos x))))
(neg.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(log (- (cos (- eps (* -1 x))) (cos x)))
(log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos x) (sin (* 1/2 eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.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))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps 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))

rewrite379.0ms (2.1%)

Memory

-22.6MiB live, 393.1MiB allocated

Rules

4 706×	`lower-*.f32`
4 676×	`lower-*.f64`
4 468×	`lower-fma.f64`
4 468×	`lower-fma.f32`
4 250×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	344
0	88	307
1	257	279
2	1756	276
0	8879	266

Stop Event

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

Counts

25 → 752

Calls

Call 1

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

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

eval203.0ms (1.1%)

Memory: 41.0MiB live, 114.2MiB allocated
Compiler: Compiled 31 378 to 3 383 computations (89.2% saved)

prune232.0ms (1.3%)

Memory

-22.2MiB live, 140.4MiB allocated

Pruning

33 alts after pruning (27 fresh and 6 done)

	Pruned	Kept	Total
New	1 285	13	1 298
Fresh	10	14	24
Picked	1	4	5
Done	1	2	3
Total	1 297	33	1 330

Accuracy

100.0%

Counts

1 330 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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))) #s(literal 2 binary64)) (.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)))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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))
	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.2%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	47.5%	(exp.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
	97.6%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 (/.f64 (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) eps) (.f64 eps eps)))
✓	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.2%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	96.9%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	96.3%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	96.3%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	48.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (neg.f64 (sin.f64 x)))))
	97.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	96.5%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	96.3%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (neg.f64 x)))))
✓	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x))))
✓	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 2 088 to 743 computations (64.4% saved)

regimes69.0ms (0.4%)

Memory

-23.4MiB live, 65.6MiB allocated

Counts

72 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (neg.f64 x)))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (neg.f64 (sin.f64 x)))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x 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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
(-.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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 (/.f64 (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) eps) (.f64 eps eps)))
(.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 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (cos (* x 2)) (neg eps)) (sin (* x -2)))) (fma.f64 eps (.f64 x #s(literal -2 binary64)) (.f64 eps (neg.f64 eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))))
(.f64 (.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 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps 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 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #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 #s(literal 1 binary64) (/.f64 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 (.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 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 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (.f64 x x)))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (.f64 (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)))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.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 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
(exp.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 eps) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (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 (+.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))) #s(literal 2 binary64)) (.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)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.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)) (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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #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 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (fma.f64 eps (neg.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))))

Outputs

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

Calls

3 calls:

33.0ms	x
18.0ms	eps
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

21.7MiB live, 59.9MiB allocated

Counts

68 → 1

Calls

Call 1

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

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)) (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))

Calls

3 calls:

17.0ms	eps
16.0ms	x
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)

regimes47.0ms (0.3%)

Memory

11.4MiB live, 50.6MiB allocated

Counts

66 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	x
16.0ms	eps
13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Memory

-33.9MiB live, 47.8MiB allocated

Counts

61 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.1%)

Memory

29.5MiB live, 29.5MiB allocated

Counts

35 → 1

Calls

Call 1

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

Outputs

(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #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
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-16.1MiB live, 23.5MiB allocated

Counts

27 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

-18.8MiB live, 20.7MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

19.1MiB live, 19.1MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-23.9MiB live, 15.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`eps`
97.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`eps`
96.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.3%	1	`x`
96.3%	1	`eps`
96.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-32.4MiB live, 8.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	eps
2.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
96.3%	1	`eps`
96.3%	1	`x`
96.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ -1 (cos eps)) (.f64 eps (.f64 eps #s(literal -1/2 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
48.7%	1	`eps`
48.7%	1	`x`
48.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

6.2MiB live, 6.2MiB 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(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #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
46.9%	1	`eps`
46.9%	1	`x`
46.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	137	521
1	192	521
2	205	521
3	212	521
4	214	521

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (6.2%)

Memory

2.4MiB live, 483.4MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
12 028×	`lower-fma.f64`
12 028×	`lower-fma.f32`
8 868×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	382
0	118	346
1	432	286
0	3627	286
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	105	498
1	277	495
2	607	495
3	2403	494
4	7863	494
0	8013	474
0	576	7019
1	1740	6651
2	4717	6617
0	8162	6218
0	606	6865
1	1971	6483
2	6230	6440
0	8638	6104
0	673	6162
1	2040	5951
2	5819	5912
0	8072	5589

Stop Event

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

Compiler

Compiled 738 to 392 computations (46.9% saved)

preprocess96.0ms (0.5%)

Memory: 2.9MiB live, 80.8MiB allocated
Compiler: Compiled 606 to 224 computations (63% 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%)

analyze43.0ms (0.2%)

sample9.9s (54.8%)

explain272.0ms (1.5%)

preprocess28.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify10.0ms (0.1%)

localize96.0ms (0.5%)

series7.0ms (0%)

simplify249.0ms (1.4%)

rewrite338.0ms (1.9%)

eval38.0ms (0.2%)

prune47.0ms (0.3%)

simplify222.0ms (1.2%)

localize429.0ms (2.4%)

series51.0ms (0.3%)

simplify241.0ms (1.3%)

rewrite223.0ms (1.2%)

eval186.0ms (1%)

prune188.0ms (1%)

simplify219.0ms (1.2%)

localize529.0ms (2.9%)

series56.0ms (0.3%)

simplify255.0ms (1.4%)

rewrite217.0ms (1.2%)

eval242.0ms (1.3%)

prune178.0ms (1%)

simplify539.0ms (3%)

localize419.0ms (2.3%)

series157.0ms (0.9%)

simplify296.0ms (1.6%)

rewrite379.0ms (2.1%)

eval203.0ms (1.1%)

prune232.0ms (1.3%)

regimes69.0ms (0.4%)

regimes50.0ms (0.3%)

regimes47.0ms (0.3%)

regimes46.0ms (0.3%)

regimes26.0ms (0.1%)

regimes22.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0%)

regimes7.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify12.0ms (0.1%)

soundness1.1s (6.2%)

preprocess96.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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