Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze74.0ms (0.4%)

Memory

-7.3MiB live, 71.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.8s (52.1%)

Memory

43.1MiB live, 11 760.6MiB allocated

Samples

3.8s	26 353×	0	invalid
3.5s	5 667×	2	valid
760.0ms	2 451×	1	valid
17.0ms	138×	0	valid

Precisions

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

ival-cos: 3.1s (48.5% of total)

const: 741.0ms (11.7% of total)

adjust: 517.0ms (8.2% of total)

ival-sub: 395.0ms (6.2% of total)

ival-<=: 390.0ms (6.2% of total)

ival-add: 312.0ms (4.9% of total)

ival-fabs: 310.0ms (4.9% of total)

ival-mult: 258.0ms (4.1% of total)

ival-<: 173.0ms (2.7% of total)

ival-and: 104.0ms (1.6% of total)

exact: 46.0ms (0.7% of total)

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

Bogosity

explain231.0ms (1.2%)

Memory

33.3MiB live, 521.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
138	1	(-4.975919485119827e-162 6.568342548944249e-163)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	139	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	138	0
-	1	117

Precision

0.9928057553956835

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	0	0
-	1	0	117

Precision?

0.9928057553956835

Recall?

1.0

Freqs

test

number	freq
0	117
1	138
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

158.0ms	356×	2	valid
24.0ms	156×	1	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-cos: 115.0ms (75.2% of total)

adjust: 22.0ms (14.4% of total)

ival-sub: 12.0ms (7.8% of total)

ival-add: 3.0ms (2% of total)

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

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

preprocess48.0ms (0.3%)

Memory

-6.4MiB live, 83.0MiB 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: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

6.0MiB live, 40.3MiB 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)

localize130.0ms (0.7%)

Memory

18.2MiB live, 251.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.030213709454007184	(cos.f64 (+.f64 x eps))
accuracy	30.500830557855423	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

111.0ms	178×	2	valid
10.0ms	78×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-cos: 54.0ms (78.3% of total)

adjust: 9.0ms (13.1% of total)

ival-sub: 4.0ms (5.8% of total)

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

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

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

series5.0ms (0%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify326.0ms (1.7%)

Memory

-53.4MiB live, 665.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite337.0ms (1.8%)

Memory

-16.4MiB live, 500.4MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval38.0ms (0.2%)

Memory: 3.2MiB live, 84.4MiB allocated
Compiler: Compiled 8 023 to 876 computations (89.1% saved)

prune34.0ms (0.2%)

Memory

10.2MiB live, 88.1MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	301	5	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	5	307

Accuracy

99.9%

Counts

307 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Compiler

Compiled 114 to 78 computations (31.6% saved)

simplify698.0ms (3.7%)

Memory

21.9MiB live, 692.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

32 044×	`lower-fma.f64`
32 044×	`lower-fma.f32`
3 244×	`lower-*.f32`
3 228×	`lower-*.f64`
2 188×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	197
0	59	187
1	90	187
2	185	187
3	344	179
4	457	179
5	652	179
6	1291	179
7	3841	179
8	6635	179
0	8140	174

Stop Event

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

Calls

Call 1

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

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

localize500.0ms (2.6%)

Memory

-3.9MiB live, 437.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.04378692720948809	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.10546875	(.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	0.23046875	(+.f64 x (+.f64 x eps))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy	13.368246249542306	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(+.f64 x eps)
accuracy	0.030213709454007184	(cos.f64 (+.f64 x eps))
accuracy	1.2961391355069525	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.500830557855423	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 eps)
accuracy	29.80129930416145	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	29.841275288955668	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
accuracy	0.0078125	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy	0.02734375	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy	0.109375	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Samples

339.0ms	177×	2	valid
74.0ms	77×	1	valid
3.0ms	2×	3	valid

Compiler

Compiled 172 to 31 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 298.0ms

ival-cos: 208.0ms (69.9% of total)

ival-mult: 42.0ms (14.1% of total)

adjust: 25.0ms (8.4% of total)

ival-add: 7.0ms (2.4% of total)

ival-sin: 7.0ms (2.4% of total)

ival-sub: 6.0ms (2% 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)

series98.0ms (0.5%)

Memory

7.0MiB live, 88.4MiB allocated

Counts

21 → 432

Calls

Call 1

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

Outputs
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -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 (* -1/2 (* (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 (* (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 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<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 (* 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 (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 (* 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 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<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))) (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 (* -1/2 (* eps (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 (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<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 (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

108 calls:

Time	Variable		Point	Expression
32.0ms	eps	@	-inf	(* (+ x (+ x eps)) 1/2)
28.0ms	eps	@	inf	(- (* eps (* -1/2 (cos x))) (sin x))
3.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	0	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)

simplify630.0ms (3.3%)

Memory

8.0MiB live, 767.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 446×	`lower-fma.f64`
14 446×	`lower-fma.f32`
6 304×	`lower-*.f64`
6 304×	`lower-*.f32`
3 656×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	3618
1	1090	3489
2	2874	3440
3	6708	3440
0	8380	3239

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 407

Calls

Call 1

Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -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)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 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)))
(* 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 (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)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -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))) (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)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

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

rewrite531.0ms (2.8%)

Memory

-48.3MiB live, 483.5MiB allocated

Rules

4 464×	`lower-fma.f64`
4 464×	`lower-fma.f32`
4 222×	`lower-*.f32`
4 206×	`lower-*.f64`
4 112×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	160
0	59	154
1	188	154
2	1452	154
0	8355	149

Stop Event

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

Counts

21 → 567

Calls

Call 1

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

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

eval253.0ms (1.3%)

Memory: 22.3MiB live, 249.9MiB allocated
Compiler: Compiled 23 636 to 2 903 computations (87.7% saved)

prune238.0ms (1.3%)

Memory

10.3MiB live, 263.4MiB allocated

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1 033	19	1 052
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 036	21	1 057

Accuracy

100.0%

Counts

1 057 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	84.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps))
▶	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
▶	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
▶	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.7%	#s(approx (- (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))))
	98.7%	#s(approx (- (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))))))
	98.0%	#s(approx (- (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))))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	97.9%	#s(approx (- (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 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps))))))

Compiler

Compiled 728 to 414 computations (43.1% saved)

simplify460.0ms (2.4%)

Memory

-14.9MiB live, 935.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

19 422×	`lower-fma.f32`
19 410×	`lower-fma.f64`
4 514×	`lower-*.f32`
4 490×	`lower-*.f64`
3 098×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	415
0	91	414
1	165	414
2	429	410
3	1038	401
4	2121	398
5	4141	395
6	7380	395
0	8089	387

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

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

localize396.0ms (2.1%)

Memory

1.8MiB live, 921.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
accuracy	0.02734375	(-.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))
accuracy	0.109375	(.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)))
accuracy	0.7661970081508973	#s(approx (* eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))
accuracy	0.11328125	(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
accuracy	0.20703125	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
accuracy	0.37109375	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.7169116773162456	#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.00390625	(.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps))
accuracy	0.17578125	(.f64 #s(literal -1/6 binary64) (.f64 x x))
accuracy	0.7170106967974174	#s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x))
accuracy	13.177911779592463	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
accuracy	0	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	29.56009769613278	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	29.630955080832386	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
accuracy	0.01953125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
accuracy	0.04378692720948809	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.10546875	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))

Samples

256.0ms	175×	2	valid
53.0ms	76×	1	valid
6.0ms	2×	3	valid
5.0ms	3×	5	exit

Compiler

Compiled 264 to 56 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 269.0ms

ival-cos: 81.0ms (30.1% of total)

ival-mult: 73.0ms (27.1% of total)

adjust: 46.0ms (17.1% of total)

ival-add: 34.0ms (12.6% of total)

ival-sin: 15.0ms (5.6% of total)

const: 11.0ms (4.1% of total)

ival-sub: 6.0ms (2.2% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series52.0ms (0.3%)

Memory

7.5MiB live, 165.8MiB allocated

Counts

25 → 516

Calls

Call 1

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

Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)>
#<alt (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (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 (* (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 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<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 (* 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 (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (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 (* (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 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<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 (* 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 (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 (* 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 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<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))) (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 (* -1/2 (* eps (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 (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<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 (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/4 eps)>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 eps)>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* 1/4 eps)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 x)>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* 1/6 (* eps x))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 (pow eps 2))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* 1/6 (* eps x))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>

Calls

129 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	(- (cos (+ x eps)) (cos x))
1.0ms	x	@	inf	(* -1/6 (* x x))
1.0ms	eps	@	-inf	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2)))
1.0ms	eps	@	inf	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2)))
1.0ms	eps	@	0	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2)))

simplify397.0ms (2.1%)

Memory

13.2MiB live, 917.0MiB allocated

Algorithm

1×	egg-herbie

Rules

13 810×	`lower-fma.f64`
13 810×	`lower-fma.f32`
7 668×	`lower-*.f64`
7 668×	`lower-*.f32`
3 072×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	439	5376
1	1355	5124
2	3859	5110
0	8308	4792

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 514

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
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(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -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))) (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)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 (pow eps 2))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(* 1/6 (* eps x))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* 1/6 (* eps x))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))

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

rewrite375.0ms (2%)

Memory

17.4MiB live, 506.3MiB allocated

Rules

5 100×	`lower-*.f32`
5 076×	`lower-*.f64`
4 144×	`lower-fma.f32`
4 132×	`lower-fma.f64`
3 522×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	364
0	91	360
1	342	356
2	2962	350
0	9264	344

Stop Event

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

Counts

25 → 520

Calls

Call 1

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

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

eval269.0ms (1.4%)

Memory: -9.2MiB live, 138.5MiB allocated
Compiler: Compiled 31 412 to 2 074 computations (93.4% saved)

prune259.0ms (1.4%)

Memory

-13.3MiB live, 130.3MiB allocated

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	1 025	9	1 034
Fresh	5	9	14
Picked	2	3	5
Done	0	2	2
Total	1 032	23	1 055

Accuracy

100.0%

Counts

1 055 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
✓	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
✓	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
✓	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.7%	#s(approx (- (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))))
	98.7%	#s(approx (- (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))))))
	98.0%	#s(approx (- (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))))
▶	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
▶	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
▶	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	97.9%	#s(approx (- (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)))))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64))))))))

Compiler

Compiled 727 to 405 computations (44.3% saved)

simplify254.0ms (1.3%)

Memory

-19.1MiB live, 259.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
cost-diff	128	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64)))
cost-diff	0	#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
cost-diff	128	(fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
cost-diff	320	(fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
cost-diff	0	(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 eps (neg.f64 x))
cost-diff	0	#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
cost-diff	0	#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))

Rules

10 798×	`lower-fma.f32`
10 784×	`lower-fma.f64`
3 234×	`lower-*.f32`
3 206×	`lower-*.f64`
3 008×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	521
0	99	517
1	196	517
2	581	508
3	1564	498
4	4042	489
5	7455	489
0	8039	474

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
(*.f64 eps (neg.f64 x))
eps
(neg.f64 x)
x
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
eps
(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
x
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))
#s(literal 1/6 binary64)
(*.f64 x x)
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
x
(fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
(.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))))
eps
#s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))
(*.f64 x x)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)))
eps
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
(*.f64 eps #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 eps)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
(*.f64 eps (neg.f64 x))
eps
(neg.f64 x)
x
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
eps
(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
x
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
#s(literal 1/6 binary64)
(*.f64 x x)
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.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)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))))
#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
x
(fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
(.f64 eps (fma.f64 x #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))))
eps
#s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))
#s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))))
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(*.f64 x x)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
eps
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
(fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
(*.f64 eps #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 eps)

localize328.0ms (1.7%)

Memory

17.5MiB live, 292.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.07421875	(.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)))
accuracy	0.35546875	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.4723373015452693	#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))
accuracy	13.177911779592463	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
accuracy	0.11328125	(.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))))
accuracy	0.37109375	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.7169116773162456	#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
accuracy	25.859055539556216	#s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))
accuracy	0.00390625	(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))
accuracy	0.01171875	(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
accuracy	0.7158843891951802	#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
accuracy	13.177911779592463	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
accuracy	0	(*.f64 eps (neg.f64 x))
accuracy	0	(neg.f64 x)
accuracy	1.2089420434442864	#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
accuracy	13.177911779592463	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
accuracy	0	#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.01953125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
accuracy	0.04378692720948809	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.10546875	(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))

Samples

198.0ms	173×	2	valid
58.0ms	79×	1	valid
6.0ms	3×	5	exit
2.0ms	1×	3	valid

Compiler

Compiled 328 to 63 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-mult: 63.0ms (29.7% of total)

ival-cos: 51.0ms (24.1% of total)

adjust: 43.0ms (20.3% of total)

ival-add: 19.0ms (9% of total)

const: 16.0ms (7.5% of total)

ival-sin: 10.0ms (4.7% of total)

ival-sub: 6.0ms (2.8% of total)

ival-neg: 3.0ms (1.4% of total)

exact: 1.0ms (0.5% of total)

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

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

series73.0ms (0.4%)

Memory

7.1MiB live, 96.3MiB allocated

Counts

27 → 576

Calls

Call 1

Inputs
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))>
#<alt (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))>
#<alt #s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))>
#<alt #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))>
#<alt (*.f64 eps (neg.f64 x))>
#<alt (neg.f64 x)>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))>
#<alt #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))>
#<alt (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))>
#<alt (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))>
#<alt (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))>
#<alt (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))>
#<alt #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))>
#<alt (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))>
#<alt #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))>
#<alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))>
#<alt (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))>
#<alt #s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))))>
#<alt (*.f64 eps #s(literal 1/6 binary64))>
#<alt (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)))>

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

Calls

144 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	(* (sin x) (neg eps))
4.0ms	eps	@	0	(* eps (neg x))
4.0ms	x	@	0	(* (sin x) (neg eps))
2.0ms	eps	@	-inf	(+ (* (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps))
1.0ms	eps	@	0	(+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))

simplify340.0ms (1.8%)

Memory

-6.7MiB live, 469.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 920×	`lower-fma.f64`
13 920×	`lower-fma.f32`
7 536×	`lower-*.f64`
7 536×	`lower-*.f32`
3 038×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	426	6121
1	1333	5809
2	3826	5771
0	8235	5411

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 576

Calls

Call 1

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

Outputs
(* -1 (* eps (sin x)))
(*.f64 eps (neg.f64 (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (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))))
(* -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)))
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(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/6 binary64) (/.f64 x eps) #s(literal -1/4 binary64)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/6 binary64) (/.f64 x eps) #s(literal -1/4 binary64)))
(* 1/4 eps)
(*.f64 eps #s(literal 1/4 binary64))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(neg.f64 (*.f64 x (fma.f64 #s(literal -1/4 binary64) (/.f64 eps x) #s(literal -1/6 binary64))))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(neg.f64 (*.f64 x (fma.f64 #s(literal -1/4 binary64) (/.f64 eps x) #s(literal -1/6 binary64))))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(neg.f64 (*.f64 x (fma.f64 #s(literal -1/4 binary64) (/.f64 eps x) #s(literal -1/6 binary64))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 (* eps x))
(.f64 eps (.f64 x #s(literal 1/6 binary64)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/4 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* 1/4 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 eps (.f64 eps (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/4 binary64))))
(* 1/4 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/4 binary64)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (* eps x))
(.f64 eps (.f64 x #s(literal 1/6 binary64)))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* 1/6 (* eps x))
(.f64 eps (.f64 x #s(literal 1/6 binary64)))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/4 binary64))) x)))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* eps (- (* 1/5040 (pow x 2)) 1/120))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* -1/120 eps)
(*.f64 eps #s(literal -1/120 binary64))
(+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(* 1/5040 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/5040 binary64)))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))
(* 1/5040 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/5040 binary64)))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))
(* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 x (.f64 x (fma.f64 #s(literal -1/120 binary64) (/.f64 eps (.f64 x x)) (.f64 eps #s(literal 1/5040 binary64)))))

rewrite290.0ms (1.5%)

Memory

0.7MiB live, 236.5MiB allocated

Rules

5 396×	`lower-*.f32`
5 368×	`lower-*.f64`
4 706×	`lower-fma.f32`
4 692×	`lower-fma.f64`
2 568×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	448
0	99	444
1	373	440
2	3244	424
0	8753	416

Stop Event

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

Counts

27 → 586

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x)))
(*.f64 eps (neg.f64 x))
(neg.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
(fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))
#s(approx (+ (* eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
(.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (*.f64 x #s(literal 1/6 binary64))))
(*.f64 eps #s(literal 1/6 binary64))
(.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)))

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(+.f64 (.f64 #s(approx (sin ( eps 1/2)) (.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 1/2)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(approx (sin ( eps 1/2)) (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 #s(approx (sin (* eps 1/2)) (.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 1/2)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(approx (sin (* eps 1/2)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))))
(.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))))
#s(approx (sin (* eps 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps x)))
#s(approx (* (sin x) (neg eps)) (*.f64 eps x))
(+.f64 (.f64 eps x) (.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 eps x) (.f64 x #s(literal 0 binary64)))
(+.f64 (.f64 eps x) (.f64 (neg.f64 x) #s(literal 0 binary64)))
(+.f64 (.f64 eps x) (.f64 #s(literal 0 binary64) (neg.f64 x)))
(+.f64 (.f64 #s(literal 0 binary64) x) (.f64 eps x))
(+.f64 (.f64 x #s(literal 0 binary64)) (.f64 eps x))
(+.f64 (.f64 (neg.f64 x) #s(literal 0 binary64)) (.f64 eps x))
(+.f64 (.f64 #s(literal 0 binary64) (neg.f64 x)) (.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(fma.f64 eps x (*.f64 #s(literal 0 binary64) x))
(fma.f64 eps x (*.f64 x #s(literal 0 binary64)))
(fma.f64 eps x (*.f64 (neg.f64 x) #s(literal 0 binary64)))
(fma.f64 eps x (*.f64 #s(literal 0 binary64) (neg.f64 x)))
(fma.f64 eps (neg.f64 x) (*.f64 #s(literal 0 binary64) x))
(fma.f64 eps (neg.f64 x) (*.f64 x #s(literal 0 binary64)))
(fma.f64 eps (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 0 binary64)))
(fma.f64 eps (neg.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 x)))
(fma.f64 #s(literal 0 binary64) x (*.f64 eps x))
(fma.f64 #s(literal 0 binary64) (neg.f64 x) (*.f64 eps x))
(fma.f64 x eps (*.f64 #s(literal 0 binary64) x))
(fma.f64 x eps (*.f64 x #s(literal 0 binary64)))
(fma.f64 x eps (*.f64 (neg.f64 x) #s(literal 0 binary64)))
(fma.f64 x eps (*.f64 #s(literal 0 binary64) (neg.f64 x)))
(fma.f64 x #s(literal 0 binary64) (*.f64 eps x))
(fma.f64 (neg.f64 x) eps (*.f64 #s(literal 0 binary64) x))
(fma.f64 (neg.f64 x) eps (*.f64 x #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) eps (*.f64 (neg.f64 x) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) eps (*.f64 #s(literal 0 binary64) (neg.f64 x)))
(fma.f64 (neg.f64 x) #s(literal 0 binary64) (*.f64 eps x))
(fma.f64 #s(literal -1 binary64) (.f64 eps x) (.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 eps x) (.f64 x #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 eps x) (.f64 (neg.f64 x) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 eps x) (.f64 #s(literal 0 binary64) (neg.f64 x)))
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(fma.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) eps (.f64 (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 0 binary64)))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 0 binary64) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) eps (*.f64 eps #s(literal -1/120 binary64)))
(fma.f64 (.f64 x #s(literal 1/5040 binary64)) (.f64 eps x) (*.f64 eps #s(literal -1/120 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) #s(literal 1/5040 binary64) (*.f64 eps #s(literal -1/120 binary64)))
(fma.f64 (.f64 eps #s(literal 1/5040 binary64)) (.f64 x x) (*.f64 eps #s(literal -1/120 binary64)))
(fma.f64 (.f64 eps (.f64 x #s(literal 1/5040 binary64))) x (*.f64 eps #s(literal -1/120 binary64)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64))) (.f64 eps (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (.f64 x x) #s(literal -1/604800 binary64))) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64)) (.f64 eps eps)) (.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))) eps))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) (.f64 eps eps)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64)) eps))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64))) (.f64 eps (.f64 eps eps)) (.f64 #s(literal -1/1728000 binary64) (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (-.f64 (.f64 (.f64 eps #s(literal -1/120 binary64)) (.f64 eps #s(literal -1/120 binary64))) (.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (*.f64 eps #s(literal -1/120 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64))))) (.f64 (.f64 eps #s(literal -1/120 binary64)) (.f64 eps #s(literal -1/120 binary64)))) (-.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps #s(literal -1/120 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))) eps)
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/128024064000 binary64)) #s(literal -1/1728000 binary64)) eps) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) eps) (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 #s(literal -1/120 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/120 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)) eps (.f64 eps (.f64 #s(literal -1/120 binary64) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/120 binary64)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) eps (.f64 (.f64 eps eps) (.f64 #s(literal -1/120 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/120 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps eps) (.f64 eps (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) eps (.f64 eps (.f64 #s(literal -1/120 binary64) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))) eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/120 binary64)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal -1/120 binary64) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)) eps (.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/120 binary64)) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/120 binary64)) (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/120 binary64)) eps (.f64 eps (.f64 (.f64 x (.f64 x #s(literal 1/5040 binary64))) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/120 binary64)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/120 binary64)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/5040 binary64)))))) (.f64 eps eps))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) eps)

eval124.0ms (0.7%)

Memory: -12.1MiB live, 101.6MiB allocated
Compiler: Compiled 37 637 to 2 213 computations (94.1% saved)

prune94.0ms (0.5%)

Memory

9.5MiB live, 99.5MiB allocated

Pruning

22 alts after pruning (13 fresh and 9 done)

	Pruned	Kept	Total
New	1 158	4	1 162
Fresh	4	9	13
Picked	1	4	5
Done	0	5	5
Total	1 163	22	1 185

Accuracy

100.0%

Counts

1 185 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
✓	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
✓	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
✓	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.7%	#s(approx (- (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))))
	98.7%	#s(approx (- (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))))))
	98.0%	#s(approx (- (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))))
	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps)) (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
✓	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
✓	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
✓	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
	97.9%	#s(approx (- (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)))))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))

Compiler

Compiled 964 to 370 computations (61.6% saved)

regimes27.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (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 (* 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 (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 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 (- (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 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.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(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.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)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps)) (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (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 ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))

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

Calls

3 calls:

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

regimes24.0ms (0.1%)

Memory

-26.4MiB live, 12.8MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (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 (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 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 (- (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 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.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(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.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)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps)) (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (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 ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( eps 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x 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)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	eps
8.0ms	x
6.0ms	(-.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)

regimes20.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (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 (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 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 (- (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 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.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(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.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)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps)) (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (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))))

Outputs
#s(approx (- (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:

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

regimes19.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (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 (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 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 (- (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 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps #s(approx (+ ( eps 1/4) (* x 1/6)) (.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(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) #s(approx (+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* eps (* eps -1/2))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.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)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx (+ ( (* x x) (+ (* (* x x) (* eps (+ (* 1/5040 (* x x)) -1/120))) (* eps 1/6))) (neg eps)) (.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/6 binary64) (/.f64 (fma.f64 eps (.f64 eps #s(literal 1/4 binary64)) (/.f64 eps (neg.f64 x))) x)))) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

-33.2MiB live, 6.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

4.0ms	eps
3.0ms	x
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (- (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:

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

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`eps`
98.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
77.7%	1	`x`
77.7%	1	`eps`
77.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
51.9%	1	`x`
51.9%	1	`eps`
51.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	269
1	114	269
2	128	269
3	135	269
4	137	269

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness894.0ms (4.7%)

Memory

16.4MiB live, 16.4MiB allocated

Rules

14 446×	`lower-fma.f64`
14 446×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 810×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	439	5376
1	1355	5124
2	3859	5110
0	8308	4792
0	360	3618
1	1090	3489
2	2874	3440
3	6708	3440
0	8380	3239
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

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

Compiler

Compiled 246 to 143 computations (41.9% saved)

preprocess109.0ms (0.6%)

Memory: -18.8MiB live, 60.8MiB allocated
Compiler: Compiled 298 to 138 computations (53.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze74.0ms (0.4%)

sample9.8s (52.1%)

explain231.0ms (1.2%)

preprocess48.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize130.0ms (0.7%)

series5.0ms (0%)

simplify326.0ms (1.7%)

rewrite337.0ms (1.8%)

eval38.0ms (0.2%)

prune34.0ms (0.2%)

simplify698.0ms (3.7%)

localize500.0ms (2.6%)

series98.0ms (0.5%)

simplify630.0ms (3.3%)

rewrite531.0ms (2.8%)

eval253.0ms (1.3%)

prune238.0ms (1.3%)

simplify460.0ms (2.4%)

localize396.0ms (2.1%)

series52.0ms (0.3%)

simplify397.0ms (2.1%)

rewrite375.0ms (2%)

eval269.0ms (1.4%)

prune259.0ms (1.4%)

simplify254.0ms (1.3%)

localize328.0ms (1.7%)

series73.0ms (0.4%)

simplify340.0ms (1.8%)

rewrite290.0ms (1.5%)

eval124.0ms (0.7%)

prune94.0ms (0.5%)

regimes27.0ms (0.1%)

regimes24.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify9.0ms (0%)

soundness894.0ms (4.7%)

preprocess109.0ms (0.6%)

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