Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze103.0ms (0.5%)

Memory

9.5MiB live, 90.0MiB 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 (51.1%)

Memory

17.5MiB live, 11 532.5MiB allocated

Samples

4.0s	26 109×	0	invalid
3.4s	5 694×	2	valid
504.0ms	2 441×	1	valid
26.0ms	121×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.0s

ival-cos: 2.7s (46% of total)

const: 891.0ms (15% of total)

adjust: 533.0ms (9% of total)

ival-add: 297.0ms (5% of total)

ival-<: 285.0ms (4.8% of total)

ival-fabs: 281.0ms (4.7% of total)

ival-sub: 277.0ms (4.7% of total)

ival-<=: 260.0ms (4.4% of total)

ival-mult: 227.0ms (3.8% of total)

ival-and: 101.0ms (1.7% of total)

exact: 47.0ms (0.8% of total)

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

Bogosity

preprocess32.0ms (0.2%)

Memory

0.8MiB live, 40.3MiB 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))

explain244.0ms (1.3%)

Memory

31.3MiB live, 147.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
132	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	132	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	132	0
-	0	124

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	0
-	0	0	124

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	124
1	130
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

180.0ms	354×	2	valid
19.0ms	154×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-cos: 148.0ms (83.9% of total)

adjust: 18.0ms (10.2% of total)

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

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

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.1%)

Memory

-26.3MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize157.0ms (0.8%)

Memory

-2.8MiB live, 119.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

118.0ms	177×	2	valid
9.0ms	77×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-cos: 75.0ms (84.4% of total)

adjust: 9.0ms (10.1% of total)

ival-sub: 3.0ms (3.4% of total)

ival-add: 2.0ms (2.3% of total)

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

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

series6.0ms (0%)

Memory

3.0MiB live, 3.0MiB 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	@	0	(- (cos (+ x eps)) (cos x))
1.0ms	x	@	0	(- (cos (+ x eps)) (cos x))
1.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
1.0ms	eps	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

simplify521.0ms (2.7%)

Memory

38.7MiB live, 593.5MiB 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)

rewrite548.0ms (2.9%)

Memory

-118.3MiB live, 595.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval39.0ms (0.2%)

Memory: -19.3MiB live, 99.6MiB allocated
Compiler: Compiled 8 023 to 876 computations (89.1% saved)

prune37.0ms (0.2%)

Memory

10.4MiB live, 127.5MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	300	6	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	300	7	307

Accuracy

99.9%

Counts

307 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	52.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
▶	99.6%	#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 175 to 118 computations (32.6% saved)

simplify821.0ms (4.3%)

Memory

-20.1MiB live, 946.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

32 648×	`lower-fma.f32`
32 644×	`lower-fma.f64`
3 244×	`lower-*.f32`
3 226×	`lower-*.f64`
2 908×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	253
0	65	253
1	118	253
2	229	253
3	480	253
4	921	253
5	1829	253
6	3536	253
7	4566	253
8	5583	253
9	6144	253
10	6238	253
11	6338	253
12	6956	253
13	7150	253
14	7154	253
15	7156	253
16	7156	253
0	8136	248

Stop Event

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

Calls

Call 1

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

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

localize309.0ms (1.6%)

Memory

13.8MiB live, 645.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
✓	accuracy	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	#s(approx (cos x) #s(literal 1 binary64))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	52.9%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
✓	accuracy	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
✓	accuracy	99.8%	(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
✓	accuracy	99.5%	(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
✓	accuracy	99.5%	(*.f64 eps #s(literal 1/24 binary64))

Samples

215.0ms	177×	2	valid
41.0ms	77×	1	valid
1.0ms	1×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 209 to 34 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 216.0ms

ival-cos: 94.0ms (43.5% of total)

adjust: 41.0ms (19% of total)

ival-mult: 41.0ms (19% of total)

ival-add: 16.0ms (7.4% of total)

const: 7.0ms (3.2% of total)

ival-sin: 7.0ms (3.2% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series57.0ms (0.3%)

Memory

24.9MiB live, 142.7MiB allocated

Counts

22 → 432

Calls

Call 1

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

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

Calls

108 calls:

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

simplify430.0ms (2.2%)

Memory

-8.5MiB live, 814.6MiB allocated

Algorithm

1×	egg-herbie

Rules

15 990×	`lower-fma.f64`
15 990×	`lower-fma.f32`
6 382×	`lower-*.f64`
6 382×	`lower-*.f32`
4 618×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	384	3977
1	1158	3942
2	3335	3868
0	8129	3669

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 425

Calls

Call 1

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

Outputs
(sin (neg x))
(sin.f64 (neg.f64 x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
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(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/6 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
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(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
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(* -1 eps)
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(* -1 eps)
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(* -1 eps)
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(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(+.f64 (cos.f64 eps) (fma.f64 (neg.f64 x) (sin.f64 eps) #s(literal -1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
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(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
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(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (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 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (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 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps 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 (.f64 eps 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 (.f64 eps 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 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps 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 (.f64 eps 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 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps 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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1 (sin x))
(sin.f64 (neg.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) eps))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
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(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* -1/36 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/30240 binary64)) #s(literal 1/720 binary64)) #s(literal -1/36 binary64))) #s(literal 1/6 binary64)))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
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(* 1/6 (sin x))
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(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (* eps (sin x)))
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(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
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(* 1/6 (* eps (sin x)))
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(* 1/6 (* eps (sin x)))
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(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps x))
(.f64 x (.f64 eps #s(literal 1/6 binary64)))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/36 binary64))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x #s(literal -1/30240 binary64)) #s(literal 1/720 binary64)) (.f64 eps #s(literal -1/36 binary64))) (*.f64 eps #s(literal 1/6 binary64))))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))

rewrite482.0ms (2.5%)

Memory

-1.8MiB live, 595.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 654×	`lower-*.f32`
5 636×	`lower-*.f64`
4 364×	`lower-fma.f32`
4 360×	`lower-fma.f64`
4 288×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	200
0	65	200
1	228	200
2	1609	200
0	8907	196

Stop Event

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

Counts

22 → 318

Calls

Call 1

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

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

eval102.0ms (0.5%)

Memory: -1.3MiB live, 208.8MiB allocated
Compiler: Compiled 19 089 to 1 568 computations (91.8% saved)

prune73.0ms (0.4%)

Memory

-4.4MiB live, 200.6MiB allocated

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	747	20	767
Fresh	0	1	1
Picked	3	2	5
Done	0	1	1
Total	750	24	774

Accuracy

100.0%

Counts

774 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.1%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x))))
▶	99.1%	#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))))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
	98.5%	#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) eps)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
▶	79.7%	#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))))))
	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
	26.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))

Compiler

Compiled 821 to 462 computations (43.7% saved)

simplify368.0ms (1.9%)

Memory

1.7MiB live, 398.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Program
✓	cost-diff	#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	(-.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	(.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	#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	(fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)
✓	cost-diff	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))
✓	cost-diff	(.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps))
✓	cost-diff	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
✓	cost-diff	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	#s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	#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))))))
✓	cost-diff	#s(approx (cos eps) #s(literal 1 binary64))
✓	cost-diff	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
✓	cost-diff	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	(.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))

Rules

12 594×	`lower-fma.f32`
12 580×	`lower-fma.f64`
3 854×	`lower-*.f32`
3 828×	`lower-*.f64`
2 660×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	416
0	86	416
1	172	416
2	392	412
3	834	412
4	1537	409
5	2298	409
6	4150	409
7	5235	409
8	6399	409
9	7181	409
10	7355	409
11	7490	409
0	8127	405

Stop Event

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

Calls

Call 1

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

localize345.0ms (1.8%)

Memory

24.9MiB live, 417.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.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))
✓	accuracy	99.8%	(.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	99.7%	#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))))
✓	accuracy	98.6%	#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	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
✓	accuracy	99.5%	(.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)
✓	accuracy	98.9%	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))
✓	accuracy	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
✓	accuracy	100.0%	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	98.7%	#s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	79.7%	#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))))))
✓	accuracy	100.0%	#s(approx (cos eps) #s(literal 1 binary64))
✓	accuracy	52.9%	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
✓	accuracy	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	99.8%	(.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	accuracy	99.5%	(*.f64 eps #s(literal 1/6 binary64))

Samples

200.0ms	177×	2	valid
74.0ms	77×	1	valid
1.0ms	1×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 279 to 50 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-cos: 73.0ms (31.9% of total)

ival-mult: 51.0ms (22.3% of total)

adjust: 36.0ms (15.8% of total)

ival-neg: 26.0ms (11.4% of total)

ival-add: 18.0ms (7.9% of total)

const: 16.0ms (7% of total)

ival-sub: 6.0ms (2.6% of total)

ival-sin: 4.0ms (1.8% of total)

exact: 1.0ms (0.4% of total)

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

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

series74.0ms (0.4%)

Memory

-6.7MiB live, 104.3MiB allocated

Counts

23 → 444

Calls

Call 1

Inputs
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))>
#<alt (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))>
#<alt (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))>
#<alt (cos.f64 x)>
#<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)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))>
#<alt #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))>
#<alt (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))>
#<alt (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))>
#<alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))>
#<alt (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps))>
#<alt #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))>
#<alt (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)>
#<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 (*.f64 eps #s(literal 1/6 binary64))>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)>
#<alt (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 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)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))))) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (- (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 (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<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 (* 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 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 (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 3))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt -1/6>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>

Calls

111 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	(+ (* (cos x) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
5.0ms	x	@	0	(* (+ (* (* x x) 1/120) -1/6) x)
4.0ms	x	@	inf	(+ (* (* x x) (* (+ (* (* x x) 1/120) -1/6) x)) x)
3.0ms	x	@	-inf	(* (+ (* (* x x) 1/120) -1/6) x)
2.0ms	x	@	inf	(* eps (+ (* (cos x) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))

simplify399.0ms (2.1%)

Memory

-31.6MiB live, 722.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 334×	`lower-fma.f64`
14 334×	`lower-fma.f32`
6 586×	`lower-*.f64`
6 586×	`lower-*.f32`
4 216×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	345	4388
1	1035	4313
2	3146	4234
0	8188	4017

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 442

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))
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1
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(- (cos eps) 1)
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1
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x
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(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos 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 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)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 3))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))

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)
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) (fma.f64 (sin.f64 eps) (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) #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 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #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 (- 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 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* 1/24 (* (pow eps 4) (cos x)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (/.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* 1/24 (* (pow eps 4) (cos x)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/6 binary64))) eps)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))))) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (.f64 x (.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (.f64 (.f64 (.f64 eps #s(literal -1/6 binary64)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(fma.f64 x (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))))) 1)))
(fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps #s(literal 1/6 binary64))) (fma.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(+ (* eps (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(fma.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/24 binary64))) (.f64 eps (.f64 eps eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (/.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
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(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(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)))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 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 x)
(*.f64 x #s(literal -1/6 binary64))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* 1/120 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/120 binary64))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* 1/120 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/120 binary64))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(* 1/120 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* 1/120 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))

rewrite405.0ms (2.1%)

Memory

13.0MiB live, 444.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 452×	`lower-*.f32`
6 426×	`lower-*.f64`
4 764×	`lower-/.f64`
4 764×	`lower-/.f32`
4 594×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	332
0	86	332
1	313	328
2	2203	328
0	9843	324

Stop Event

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

Counts

23 → 344

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (cos.f64 x) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(+.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)) (.f64 (sin.f64 x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(+.f64 (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)) (.f64 (sin.f64 x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))))
(fma.f64 eps (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 eps (sin.f64 x)) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) eps (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) eps (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
(fma.f64 (.f64 eps (cos.f64 x)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)))
(fma.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (sin.f64 x) (.f64 (cos.f64 x) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))
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(.f64 (-.f64 (.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)))) #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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 x) #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 x (.f64 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 #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 x #s(literal -1/6 binary64)))
(+.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) (.f64 #s(literal -1/6 binary64) x))
(fma.f64 x #s(literal -1/6 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64)) (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) x (.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) x))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x (*.f64 #s(literal -1/6 binary64) x))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64))) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) x)) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal -1/6 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64)) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64)))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 x #s(literal -1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) (-.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 x #s(literal -1/6 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/6 binary64) x) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x)) (.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) (-.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/6 binary64) x)) (.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x) (.f64 #s(literal -1/6 binary64) x)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/120 binary64)) x #s(literal -1/6 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)) (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) #s(literal 1/36 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) #s(literal -1/10077696 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (-.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/373248000 binary64)))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) #s(literal 1/46656 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) #s(literal -1/216 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) #s(literal 1/46656 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (+.f64 #s(literal 1/1296 binary64) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) #s(literal 1/36 binary64)))) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) #s(literal 1/1296 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal 1/36 binary64)) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)))) (neg.f64 (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal 1/6 binary64))))

eval125.0ms (0.7%)

Memory: 10.5MiB live, 85.4MiB allocated
Compiler: Compiled 22 353 to 1 566 computations (93% saved)

prune174.0ms (0.9%)

Memory

-7.9MiB live, 121.2MiB allocated

Pruning

28 alts after pruning (21 fresh and 7 done)

	Pruned	Kept	Total
New	771	15	786
Fresh	10	6	16
Picked	1	4	5
Done	0	3	3
Total	782	28	810

Accuracy

100.0%

Counts

810 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.1%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.1%	#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 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.0%	#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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
✓	99.1%	#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))))
▶	99.2%	#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))))
	98.5%	#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) eps)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.8%	#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))))
	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
▶	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	51.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
▶	23.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
	97.9%	#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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
	26.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* (cos x) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))))

Compiler

Compiled 922 to 497 computations (46.1% saved)

simplify423.0ms (2.2%)

Memory

-20.5MiB live, 257.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (* eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(-.f64 #s(approx (* eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #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 #s(literal -1/2 binary64))) (sin.f64 x))))
✓	cost-diff	0	#s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))
✓	cost-diff	0	#s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x))))))
✓	cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
✓	cost-diff	1152	(.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x))))
✓	cost-diff	0	(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)
✓	cost-diff	0	#s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps))
✓	cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
✓	cost-diff	0	(neg.f64 eps)
✓	cost-diff	0	(*.f64 x (neg.f64 eps))
✓	cost-diff	0	#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
✓	cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))

Rules

12 142×	`lower-fma.f32`
12 140×	`lower-fma.f64`
4 636×	`lower-*.f32`
4 610×	`lower-*.f64`
1 356×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	394
0	79	368
1	149	368
2	372	360
3	773	352
4	1391	340
5	4611	340
0	8234	335

Stop Event

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

Calls

Call 1

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

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

localize389.0ms (2%)

Memory

17.1MiB live, 292.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(approx (* eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
✓	accuracy	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))))
✓	accuracy	98.0%	#s(approx (* eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	85.5%	#s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))
✓	accuracy	84.2%	#s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x))))))
✓	accuracy	71.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
✓	accuracy	54.8%	(/.f64 eps (*.f64 x x))
✓	accuracy	100.0%	(.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)
✓	accuracy	98.7%	#s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps))
✓	accuracy	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
✓	accuracy	100.0%	(*.f64 x (neg.f64 eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	97.9%	#s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps)))
✓	accuracy	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
✓	accuracy	100.0%	(.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))
✓	accuracy	99.9%	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(.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	99.6%	(+.f64 x (+.f64 x eps))

Samples

206.0ms	176×	2	valid
39.0ms	76×	1	valid
1.0ms	3×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 249 to 46 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

ival-cos: 67.0ms (35.4% of total)

ival-mult: 43.0ms (22.7% of total)

adjust: 30.0ms (15.8% of total)

ival-add: 26.0ms (13.7% of total)

ival-sub: 8.0ms (4.2% of total)

ival-sin: 7.0ms (3.7% of total)

const: 4.0ms (2.1% of total)

ival-div: 3.0ms (1.6% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series98.0ms (0.5%)

Memory

-5.5MiB live, 41.3MiB allocated

Counts

23 → 516

Calls

Call 1

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

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

Calls

129 calls:

Time	Variable		Point	Expression
35.0ms	x	@	-inf	(* x (* eps (+ (* x (* x 1/6)) -1)))
2.0ms	eps	@	inf	(* (* x (* x x)) (- (* eps 1/6) (/ eps (* x x))))
1.0ms	eps	@	0	(* (* x (* x x)) (- (* eps 1/6) (/ eps (* x x))))
1.0ms	eps	@	-inf	(* (* x (* x x)) (- (* eps 1/6) (/ eps (* x x))))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)

simplify502.0ms (2.6%)

Memory

14.7MiB live, 171.8MiB allocated

Algorithm

1×	egg-herbie

Rules

14 486×	`lower-fma.f64`
14 486×	`lower-fma.f32`
6 102×	`lower-*.f64`
6 102×	`lower-*.f32`
3 164×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	314	4643
1	981	4414
2	2710	4288
3	6524	4288
0	8126	4122

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 498

Calls

Call 1

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

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

rewrite361.0ms (1.9%)

Memory

2.4MiB live, 390.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 834×	`lower-/.f32`
4 832×	`lower-/.f64`
4 812×	`lower-*.f32`
4 786×	`lower-*.f64`
3 268×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	329
0	79	312
1	267	304
2	2009	304
0	8864	292

Stop Event

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

Counts

23 → 433

Calls

Call 1

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

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

eval98.0ms (0.5%)

Memory: 6.9MiB live, 174.4MiB allocated
Compiler: Compiled 17 831 to 1 901 computations (89.3% saved)

prune88.0ms (0.5%)

Memory

-20.1MiB live, 222.4MiB allocated

Pruning

30 alts after pruning (20 fresh and 10 done)

	Pruned	Kept	Total
New	925	6	931
Fresh	2	14	16
Picked	2	3	5
Done	0	7	7
Total	929	30	959

Accuracy

100.0%

Counts

959 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.1%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))
	82.5%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (.f64 eps eps)) eps))
	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	51.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.1%	#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 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.0%	#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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
✓	99.1%	#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))))
✓	99.2%	#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))))
	98.5%	#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) eps)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
	51.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
✓	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
	26.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* (cos x) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))))

Compiler

Compiled 1 315 to 493 computations (62.5% saved)

regimes38.0ms (0.2%)

Memory

-1.5MiB live, 76.8MiB allocated

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
#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)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))
#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 (.f64 (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (.f64 eps eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 #s(literal 1/1440 binary64) (.f64 x x) #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 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 (cos.f64 x) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* (cos x) (* eps (+ (* 1/24 (* eps eps)) -1/2))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))

Outputs

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

Calls

3 calls:

13.0ms	x
12.0ms	eps
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

7.0MiB live, 87.7MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
#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)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))
#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 (.f64 (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (.f64 eps eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 #s(literal 1/1440 binary64) (.f64 x x) #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 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.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))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

7.9MiB live, 86.4MiB allocated

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
#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)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))
#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 (.f64 (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (.f64 eps eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 #s(literal 1/1440 binary64) (.f64 x x) #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))))

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:

11.0ms	x
11.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

9.0MiB live, 94.0MiB allocated

Counts

41 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
#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)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))
#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 (.f64 (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (.f64 eps eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (fma.f64 (.f64 x x) (fma.f64 eps #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 #s(literal -1/2 binary64) eps))) (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 #s(literal 1/1440 binary64) (.f64 x x) #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
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* eps (* -1/2 (cos x))) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))))

Calls

3 calls:

13.0ms	eps
10.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.1%)

Memory

-0.9MiB live, 77.8MiB 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 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))
#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 #s(literal -1/2 binary64) eps)) (sin.f64 x))))

Calls

3 calls:

9.0ms	eps
8.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

Memory

-9.4MiB live, 72.4MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.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 #s(literal -1/2 binary64) eps) 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)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x #s(approx ( eps (+ (* x (* x 1/6)) -1)) (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 #s(approx ( x (+ (* 1/6 (* x x)) -1)) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))) eps)))
#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 (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (fma.f64 (.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps)) x (.f64 x (neg.f64 eps)))))
#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 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) 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 (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) #s(approx (* x (* eps (+ (* x (* x 1/6)) -1))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/6 binary64)) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (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)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 x x) (.f64 eps (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #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 #s(approx (sin x) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)))))) (-.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)))))) (neg.f64 eps)))

Outputs

#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 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))))

Calls

3 calls:

9.0ms	x
8.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

9.8MiB live, 49.2MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-23.3MiB live, 16.5MiB 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 x (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.4%	1	`x`
79.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.4%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

12.9MiB live, 12.8MiB 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	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
51.9%	1	`eps`
51.9%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-9.4MiB live, 29.9MiB allocated

Algorithm

1×	egg-herbie

Rules

46×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	216
1	114	216
2	133	216
3	142	216
4	145	216

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (6.6%)

Memory

-2.5MiB live, 838.9MiB allocated

Rules

15 990×	`lower-fma.f64`
15 990×	`lower-fma.f32`
14 486×	`lower-fma.f64`
14 486×	`lower-fma.f32`
14 334×	`lower-fma.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
0	384	3977
1	1158	3942
2	3335	3868
0	8129	3669
0	314	4643
1	981	4414
2	2710	4288
3	6524	4288
0	8126	4122
0	55	329
0	79	312
1	267	304
2	2009	304
0	8864	292
0	345	4388
1	1035	4313
2	3146	4234
0	8188	4017
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×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 243 to 143 computations (41.2% saved)

preprocess60.0ms (0.3%)

Memory: 22.0MiB live, 61.4MiB allocated
Compiler: Compiled 306 to 154 computations (49.7% 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%)

analyze103.0ms (0.5%)

sample9.8s (51.1%)

preprocess32.0ms (0.2%)

explain244.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.1%)

localize157.0ms (0.8%)

series6.0ms (0%)

simplify521.0ms (2.7%)

rewrite548.0ms (2.9%)

eval39.0ms (0.2%)

prune37.0ms (0.2%)

simplify821.0ms (4.3%)

localize309.0ms (1.6%)

series57.0ms (0.3%)

simplify430.0ms (2.2%)

rewrite482.0ms (2.5%)

eval102.0ms (0.5%)

prune73.0ms (0.4%)

simplify368.0ms (1.9%)

localize345.0ms (1.8%)

series74.0ms (0.4%)

simplify399.0ms (2.1%)

rewrite405.0ms (2.1%)

eval125.0ms (0.7%)

prune174.0ms (0.9%)

simplify423.0ms (2.2%)

localize389.0ms (2%)

series98.0ms (0.5%)

simplify502.0ms (2.6%)

rewrite361.0ms (1.9%)

eval98.0ms (0.5%)

prune88.0ms (0.5%)

regimes38.0ms (0.2%)

regimes35.0ms (0.2%)

regimes33.0ms (0.2%)

regimes35.0ms (0.2%)

regimes27.0ms (0.1%)

regimes25.0ms (0.1%)

regimes16.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify10.0ms (0.1%)

soundness1.3s (6.6%)

preprocess60.0ms (0.3%)

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