Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze40.0ms (0.3%)

Memory

21.4MiB live, 59.4MiB 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)

sample5.8s (40.7%)

Memory

-10.4MiB live, 7 644.3MiB allocated

Samples

3.0s	26 541×	0	invalid
592.0ms	5 543×	0	valid
508.0ms	2 713×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

const: 602.0ms (21.1% of total)

ival-sin: 578.0ms (20.2% of total)

ival-mult: 313.0ms (11% of total)

ival-<=: 266.0ms (9.3% of total)

ival-fabs: 246.0ms (8.6% of total)

ival-add: 216.0ms (7.6% of total)

ival-sub: 205.0ms (7.2% of total)

ival-<: 205.0ms (7.2% of total)

ival-and: 100.0ms (3.5% of total)

adjust: 69.0ms (2.4% of total)

exact: 45.0ms (1.6% of total)

ival-assert: 14.0ms (0.5% of total)

Bogosity

explain97.0ms (0.7%)

Memory

-7.1MiB live, 124.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	2	(-4.8350388337660666e-294 4.7922708044239923e-296)	2	(4.758618899348653e-110 7.457063275209576e-112)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	224	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	222	3
-	2	29

Precision

0.9910714285714286

Recall

0.9866666666666667

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	222	3	0
-	2	6	23

Precision?

0.9656652360515021

Recall?

1.0

Freqs

test

number	freq
0	32
1	223
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms	324×	0	valid
22.0ms	186×	1	valid
0.0ms	2×	2	valid

Compiler

Compiled 69 to 28 computations (59.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-sin: 27.0ms (71.6% of total)

adjust: 4.0ms (10.6% of total)

ival-add: 3.0ms (8% of total)

ival-sub: 3.0ms (8% of total)

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

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

preprocess27.0ms (0.2%)

Memory

5.5MiB live, 42.1MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sin.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.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 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

localize26.0ms (0.2%)

Memory

10.4MiB live, 48.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.050411667988352074	(sin.f64 (+.f64 x eps))
accuracy	25.29601033883331	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

9.0ms	93×	1	valid
8.0ms	162×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 4.0ms (41.4% of total)

adjust: 2.0ms (20.7% of total)

ival-add: 2.0ms (20.7% of total)

ival-sub: 2.0ms (20.7% of total)

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

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

series6.0ms (0%)

Memory

-36.4MiB live, 7.4MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify391.0ms (2.8%)

Memory

-4.3MiB live, 524.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (fma.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 #s(literal 1/6 binary64) (*.f64 x x))))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 (cos.f64 eps) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 (.f64 eps (cos.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.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)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(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)

rewrite313.0ms (2.2%)

Memory

13.1MiB live, 480.4MiB allocated

Rules

4 986×	`lower-fma.f64`
4 986×	`lower-fma.f32`
4 676×	`lower-*.f64`
4 676×	`lower-*.f32`
2 176×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

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

eval48.0ms (0.3%)

Memory: 14.2MiB live, 50.9MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune51.0ms (0.4%)

Memory

21.9MiB live, 60.0MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	283	8	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	283	9	292

Accuracy

100.0%

Counts

292 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
▶	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	59.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 223 to 144 computations (35.4% saved)

simplify610.0ms (4.3%)

Memory

-4.5MiB live, 363.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) 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))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

7 910×	`lower-fma.f32`
7 902×	`lower-fma.f64`
6 388×	`lower-*.f32`
6 376×	`lower-*.f64`
2 348×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	207
0	68	185
1	103	185
2	168	183
3	236	179
4	369	179
5	703	179
6	2098	179
7	2842	179
8	4063	179
9	4693	179
10	5057	179
11	5455	179
12	5811	179
13	6001	179
14	6095	179
15	6125	179
16	7332	179
0	8122	175

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

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

localize254.0ms (1.8%)

Memory

-27.3MiB live, 167.4MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	0.006191259768442017	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
accuracy	18.953971220870933	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
accuracy	0.050411667988352074	(sin.f64 (+.f64 x eps))
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
accuracy	25.29601033883331	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
accuracy	0.050411667988352074	(sin.f64 (+.f64 x eps))
accuracy	0.09765625	(.f64 x (.f64 x x))
accuracy	0.802912900379896	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	25.29601033883331	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
accuracy	0	(sin.f64 eps)
accuracy	0.998403535828387	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04675260466091879	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

182.0ms	216×	1	valid
25.0ms	31×	2	valid
2.0ms	9×	0	valid

Compiler

Compiled 197 to 37 computations (81.2% saved)

Precisions

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

adjust: 41.0ms (23.3% of total)

const: 40.0ms (22.7% of total)

ival-add: 30.0ms (17% of total)

ival-sin: 23.0ms (13.1% of total)

ival-mult: 22.0ms (12.5% of total)

ival-cos: 10.0ms (5.7% of total)

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

ival-sub: 2.0ms (1.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory

0.5MiB live, 38.6MiB allocated

Counts

20 → 396

Calls

Call 1

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

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 (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- 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 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 (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (/ 1 (sin eps))>
#<alt (+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))>
#<alt (/ 1 (* eps (cos x)))>
#<alt (/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)>
#<alt (/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)>
#<alt (/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* x (- (cos eps) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (cos x))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (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 (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt 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)>

Calls

99 calls:

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

simplify509.0ms (3.6%)

Memory

26.1MiB live, 591.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 146×	`lower-fma.f64`
14 146×	`lower-fma.f32`
6 098×	`lower-*.f64`
6 098×	`lower-*.f32`
5 990×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	3851
1	1275	3670
2	3532	3575
0	8501	3312

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 373

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
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- 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)))
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)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(/ 1 (sin eps))
(+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (* eps (cos x)))
(/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
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 (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
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)

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

rewrite568.0ms (4%)

Memory

3.2MiB live, 435.9MiB allocated

Rules

5 262×	`lower-fma.f32`
5 254×	`lower-fma.f64`
5 126×	`lower-*.f32`
5 114×	`lower-*.f64`
4 696×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	155
0	68	131
1	228	131
2	1741	131
0	9666	131

Stop Event

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

Counts

20 → 900

Calls

Call 1

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

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

eval253.0ms (1.8%)

Memory: -12.9MiB live, 213.1MiB allocated
Compiler: Compiled 45 977 to 2 931 computations (93.6% saved)

prune157.0ms (1.1%)

Memory

22.3MiB live, 272.7MiB allocated

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	1 416	14	1 430
Fresh	3	0	3
Picked	3	2	5
Done	0	1	1
Total	1 422	17	1 439

Accuracy

100.0%

Counts

1 439 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 (neg.f64 x)))) (*.f64 (sin.f64 eps) (cos.f64 x)))
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))))) (-.f64 (sin.f64 (neg.f64 x)) (.f64 (sin.f64 x) (cos.f64 eps)))))
▶	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
✓	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	59.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.5%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	99.5%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
▶	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 646 to 388 computations (39.9% saved)

simplify301.0ms (2.1%)

Memory

-2.8MiB live, 351.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
cost-diff	128	(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

9 646×	`lower-fma.f32`
9 634×	`lower-fma.f64`
4 236×	`lower-*.f32`
4 200×	`lower-*.f64`
2 158×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	493
0	103	458
1	183	413
2	427	410
3	1197	410
4	2240	410
5	2810	410
6	3335	410
7	3907	410
8	4636	410
9	5240	410
10	5980	410
11	7482	410
0	8374	398

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

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

localize273.0ms (1.9%)

Memory

2.6MiB live, 400.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.006191259768442017	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
accuracy	0.01171875	(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
accuracy	0.06640625	(fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
accuracy	0.3163445163266936	#s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)))
accuracy	0.00390625	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.0078125	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
accuracy	0.014003759768442018	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.04675260466091879	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.00390625	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04675260466091879	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.3076390084754006	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	60.60729367702476	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
accuracy	0	(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
accuracy	0.0078125	(.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.015625	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

162.0ms	216×	1	valid
34.0ms	31×	2	valid
4.0ms	9×	0	valid

Compiler

Compiled 425 to 55 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-mult: 49.0ms (31.6% of total)

adjust: 31.0ms (20% of total)

ival-sin: 23.0ms (14.9% of total)

ival-cos: 16.0ms (10.3% of total)

const: 16.0ms (10.3% of total)

ival-add: 16.0ms (10.3% of total)

ival-sub: 2.0ms (1.3% of total)

exact: 1.0ms (0.6% of total)

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

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

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

series25.0ms (0.2%)

Memory

-0.5MiB live, 37.8MiB allocated

Counts

25 → 492

Calls

Call 1

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

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (cos x))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
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#<alt (* 1/2 eps)>
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#<alt -1/48>
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#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>

Calls

123 calls:

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

simplify396.0ms (2.8%)

Memory

-0.2MiB live, 639.8MiB allocated

Algorithm

1×	egg-herbie

Rules

15 160×	`lower-fma.f64`
15 160×	`lower-fma.f32`
5 910×	`lower-*.f64`
5 910×	`lower-*.f32`
5 360×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	433	5880
1	1346	5580
2	3925	5371
0	8108	5041

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 464

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
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)
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(cos x)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
1
(+ 1 (* -1/8 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))) (cos.f64 x))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 0 binary64))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps x))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(.f64 x (fma.f64 (.f64 x (.f64 x eps)) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))) (.f64 eps #s(literal 1/12 binary64))) (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))

rewrite351.0ms (2.5%)

Memory

-10.0MiB live, 544.0MiB allocated

Rules

4 756×	`lower-*.f32`
4 720×	`lower-*.f64`
3 940×	`lower-/.f64`
3 940×	`lower-/.f32`
3 456×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	366
0	103	339
1	324	266
2	2686	266
0	8856	257

Stop Event

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

Counts

25 → 440

Calls

Call 1

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

Outputs
x
(*.f64 x #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) x)
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
eps
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.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 eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.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 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (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 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (.f64 (-.f64 #s(literal 0 binary64) 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 (.f64 eps eps)))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) 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 eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))) (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))
(fma.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))
(fma.f64 #s(literal -1 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x)))))))
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(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64))) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) #s(literal 1/2304 binary64))) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal -1/2304 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2304 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))))) (neg.f64 (-.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))) (fma.f64 (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal -1/2304 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))))
(.f64 (fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64))))
#s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 #s(literal 0 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 #s(literal 0 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x) (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 0 binary64)))
(fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64) (.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(/.f64 (.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (neg.f64 eps))
(/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 eps eps)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (neg.f64 (*.f64 eps eps)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))
(.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
(.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64))

eval142.0ms (1%)

Memory: 4.5MiB live, 232.9MiB allocated
Compiler: Compiled 30 587 to 2 371 computations (92.2% saved)

prune106.0ms (0.8%)

Memory

-12.3MiB live, 213.9MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	1 032	7	1 039
Fresh	4	5	9
Picked	4	1	5
Done	0	3	3
Total	1 040	16	1 056

Accuracy

100.0%

Counts

1 056 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
	99.7%	(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
✓	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	59.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
▶	99.5%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x)))))) #s(literal 2 binary64))
	99.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
▶	99.5%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
✓	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 524 to 317 computations (39.5% saved)

simplify330.0ms (2.3%)

Memory

22.5MiB live, 492.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
cost-diff	0	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
cost-diff	0	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
cost-diff	0	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) eps x)
cost-diff	0	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff	0	(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
cost-diff	0	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
cost-diff	0	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
cost-diff	128	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x)))
cost-diff	128	(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x))))) #s(literal 2 binary64))

Rules

15 120×	`lower-fma.f32`
15 106×	`lower-fma.f64`
3 174×	`lower-*.f32`
3 142×	`lower-*.f64`
1 996×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	540
0	110	510
1	199	510
2	459	507
3	945	497
4	1481	495
5	2408	495
6	3112	495
7	4392	495
8	6090	492
0	8024	476

Stop Event

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

Calls

Call 1

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

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

localize217.0ms (1.5%)

Memory

-5.6MiB live, 273.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
accuracy	0.0078125	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
accuracy	0.3357085950267026	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
accuracy	0.00390625	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.014003759768442018	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) #s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
accuracy	0.04675260466091879	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.10773770623272953	#s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.00390625	(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.04675260466091879	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.3076390084754006	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0	(*.f64 eps eps)
accuracy	0.13356428636499235	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
accuracy	0.1953125	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
accuracy	0.998403535828387	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
accuracy	0.01171875	(+.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.015625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (neg.f64 x)))
accuracy	0.042744197286481406	(cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))
accuracy	0.04675260466091879	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

115.0ms	214×	0	valid
36.0ms	42×	1	valid

Compiler

Compiled 417 to 65 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult: 41.0ms (34.9% of total)

ival-cos: 24.0ms (20.4% of total)

ival-add: 15.0ms (12.8% of total)

ival-sin: 13.0ms (11.1% of total)

const: 13.0ms (11.1% of total)

adjust: 5.0ms (4.3% of total)

ival-div: 4.0ms (3.4% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

ival-neg: 1.0ms (0.9% of total)

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

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

series33.0ms (0.2%)

Memory

-8.2MiB live, 32.2MiB allocated

Counts

28 → 540

Calls

Call 1

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

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* eps (+ (* 2 (* eps (+ (* -1/48 (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x))))) (* 1/2 (+ (* -1/2 (+ (* -1/48 (sin x)) (* 1/48 (sin x)))) (* -1/48 (sin (neg x)))))))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps))))>
#<alt (+ (* 2 (* x (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))>
#<alt (+ (* x (+ (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) (* x (* (sin (* 1/2 eps)) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))>
#<alt (+ (* x (+ (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) (* x (+ (* 2 (* x (* (sin (* 1/2 eps)) (+ (* -1/2 (+ (* -1/6 (sin (* -1/2 eps))) (* -1/6 (sin (* 1/2 eps))))) (* 1/6 (sin (* 1/2 eps))))))) (* (sin (* 1/2 eps)) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps))))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1/2 eps)>
#<alt (+ x (* -1/2 eps))>
#<alt (+ x (* -1/2 eps))>
#<alt (+ x (* -1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps x))))>
#<alt (* x (+ 1 (* -1/2 (/ eps x))))>
#<alt (* x (+ 1 (* -1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* -1/2 eps))>
#<alt (+ x (* -1/2 eps))>
#<alt (+ x (* -1/2 eps))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (/ x eps) 1/2))>
#<alt (* eps (- (/ x eps) 1/2))>
#<alt (* eps (- (/ x eps) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* 1/2 (* eps (sin (neg x))))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (sin (neg x)))) (* 1/2 (sin (neg x)))))>
#<alt (* eps (+ (* 1/2 (sin (neg x))) (* (pow eps 2) (+ (* -1/48 (sin (neg x))) (* 1/3840 (* (pow eps 2) (sin (neg x))))))))>
#<alt (* eps (+ (* 1/2 (sin (neg x))) (* (pow eps 2) (+ (* -1/48 (sin (neg x))) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin (neg x)))) (* 1/3840 (sin (neg x)))))))))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* -1 (* x (sin (* 1/2 eps))))>
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* 1/6 (* (pow x 2) (sin (* 1/2 eps))))))>
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/6 (sin (* 1/2 eps)))))))>
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* 1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* 1/2 eps))))))))))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (neg x)) (sin (* 1/2 eps)))>
#<alt (* (sin (* -1 x)) (sin (* 1/2 eps)))>
#<alt (* (sin (* -1 x)) (sin (* 1/2 eps)))>
#<alt (* (sin (* -1 x)) (sin (* 1/2 eps)))>
#<alt (* (sin (* -1 x)) (sin (* 1/2 eps)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 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 (* 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 (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (cos (* -1/2 eps))>
#<alt (+ (cos (* -1/2 eps)) (* -1 (* x (sin (* -1/2 eps)))))>
#<alt (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (sin (* -1/2 eps)))))>
#<alt (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* 1/6 (* x (sin (* -1/2 eps)))))) (sin (* -1/2 eps)))))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (- (* -1/2 eps) (* -1 x)))>
#<alt (cos (- (* -1/2 eps) (* -1 x)))>
#<alt (cos (- (* -1/2 eps) (* -1 x)))>
#<alt (cos (- (* -1/2 eps) (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* 1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* -1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* -1/48 (* eps (sin x))))) (* -1/2 (sin x)))))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (* 2 (cos x))>
#<alt (+ (* -1 (* eps (+ (* -1/2 (sin x)) (* 1/2 (sin x))))) (* 2 (cos x)))>
#<alt (+ (* 2 (cos x)) (* eps (- (* -1/4 (* eps (cos x))) (+ (* -1/2 (sin x)) (* 1/2 (sin x))))))>
#<alt (+ (* 2 (cos x)) (* eps (- (* eps (+ (* -1 (* eps (+ (* -1/48 (sin x)) (* 1/48 (sin x))))) (* -1/4 (cos x)))) (+ (* -1/2 (sin x)) (* 1/2 (sin x))))))>
#<alt (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))>
#<alt (+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* -1 (* x (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))>
#<alt (+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps))))) (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))>
#<alt (+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1 (* x (+ (* -1/6 (sin (* -1/2 eps))) (* -1/6 (sin (* 1/2 eps)))))) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps)))))) (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
#<alt (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
#<alt (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt -1/48>
#<alt (- (* 1/3840 (pow eps 2)) 1/48)>
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)>
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (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

135 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2)
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2)
1.0ms	eps	@	0	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2)

simplify327.0ms (2.3%)

Memory

11.7MiB live, 321.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 390×	`lower-fma.f64`
8 390×	`lower-fma.f32`
6 040×	`lower-*.f64`
6 040×	`lower-*.f32`
1 954×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	536	5826
1	1728	5587
2	5274	5494
0	8211	5043

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 516

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* eps (+ (* 2 (* eps (+ (* -1/48 (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x))))) (* 1/2 (+ (* -1/2 (+ (* -1/48 (sin x)) (* 1/48 (sin x)))) (* -1/48 (sin (neg x)))))))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))
(+ (* x (+ (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) (* x (* (sin (* 1/2 eps)) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))
(+ (* x (+ (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) (* x (+ (* 2 (* x (* (sin (* 1/2 eps)) (+ (* -1/2 (+ (* -1/6 (sin (* -1/2 eps))) (* -1/6 (sin (* 1/2 eps))))) (* 1/6 (sin (* 1/2 eps))))))) (* (sin (* 1/2 eps)) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps))))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))) (* (sin (* -1 x)) (sin (* 1/2 eps))))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1/2 eps)
(+ x (* -1/2 eps))
(+ x (* -1/2 eps))
(+ x (* -1/2 eps))
x
(* x (+ 1 (* -1/2 (/ eps x))))
(* x (+ 1 (* -1/2 (/ eps x))))
(* x (+ 1 (* -1/2 (/ eps x))))
x
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
x
(+ x (* -1/2 eps))
(+ x (* -1/2 eps))
(+ x (* -1/2 eps))
(* -1/2 eps)
(* eps (- (/ x eps) 1/2))
(* eps (- (/ x eps) 1/2))
(* eps (- (/ x eps) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))
(* 1/2 (* eps (sin (neg x))))
(* eps (+ (* -1/48 (* (pow eps 2) (sin (neg x)))) (* 1/2 (sin (neg x)))))
(* eps (+ (* 1/2 (sin (neg x))) (* (pow eps 2) (+ (* -1/48 (sin (neg x))) (* 1/3840 (* (pow eps 2) (sin (neg x))))))))
(* eps (+ (* 1/2 (sin (neg x))) (* (pow eps 2) (+ (* -1/48 (sin (neg x))) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin (neg x)))) (* 1/3840 (sin (neg x)))))))))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* -1 (* x (sin (* 1/2 eps))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* 1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/6 (sin (* 1/2 eps)))))))
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* 1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* 1/2 eps))))))))))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (neg x)) (sin (* 1/2 eps)))
(* (sin (* -1 x)) (sin (* 1/2 eps)))
(* (sin (* -1 x)) (sin (* 1/2 eps)))
(* (sin (* -1 x)) (sin (* 1/2 eps)))
(* (sin (* -1 x)) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(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 (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 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)))
(* 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 (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* -1 (* x (sin (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (sin (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* 1/6 (* x (sin (* -1/2 eps)))))) (sin (* -1/2 eps)))))
(cos (+ x (* -1/2 eps)))
(cos (+ x (* -1/2 eps)))
(cos (+ x (* -1/2 eps)))
(cos (+ x (* -1/2 eps)))
(cos (- (* -1/2 eps) (* -1 x)))
(cos (- (* -1/2 eps) (* -1 x)))
(cos (- (* -1/2 eps) (* -1 x)))
(cos (- (* -1/2 eps) (* -1 x)))
(cos x)
(+ (cos x) (* 1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* -1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* -1/48 (* eps (sin x))))) (* -1/2 (sin x)))))
(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)))
(* 2 (cos x))
(+ (* -1 (* eps (+ (* -1/2 (sin x)) (* 1/2 (sin x))))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (- (* -1/4 (* eps (cos x))) (+ (* -1/2 (sin x)) (* 1/2 (sin x))))))
(+ (* 2 (cos x)) (* eps (- (* eps (+ (* -1 (* eps (+ (* -1/48 (sin x)) (* 1/48 (sin x))))) (* -1/4 (cos x)))) (+ (* -1/2 (sin x)) (* 1/2 (sin x))))))
(+ (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))))
(+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))
(+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* -1 (* x (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps))))) (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (cos (* -1/2 eps)) (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1 (* x (+ (* -1/6 (sin (* -1/2 eps))) (* -1/6 (sin (* 1/2 eps)))))) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps)))))) (+ (sin (* -1/2 eps)) (sin (* 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 (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))
(+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))
(+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))
(+ (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (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
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x)))))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (+ (* 1/2 (sin (neg x))) (* eps (+ (* 2 (* eps (+ (* -1/48 (+ (* -1/2 (+ (* -1/2 (sin x)) (* 1/2 (sin x)))) (* 1/2 (sin (neg x))))) (* 1/2 (+ (* -1/2 (+ (* -1/48 (sin x)) (* 1/48 (sin x)))) (* -1/48 (sin (neg x)))))))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/96 binary64) (.f64 (sin.f64 x) #s(literal 1/96 binary64))) (.f64 eps #s(literal 2 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (+ (* 1/2 (+ (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))) (* (sin (neg x)) (sin (* 1/2 eps))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* 2 (* x (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (+ (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) (* x (* (sin (* 1/2 eps)) (+ (* -1/2 (cos (* -1/2 eps))) (* -1/2 (cos (* 1/2 eps)))))))) (* (sin (* 1/2 eps)) (+ (cos (* -1/2 eps)) (cos (* 1/2 eps)))))
(fma.f64 x (fma.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (.f64 #s(literal 2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
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(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) #s(literal -1/645120 binary64)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) #s(literal -1/645120 binary64)))
(* -1/645120 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) #s(literal -1/645120 binary64)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) #s(literal -1/645120 binary64)))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 x (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (cos.f64 x) (.f64 eps #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (neg.f64 (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #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 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x 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)

rewrite332.0ms (2.3%)

Memory

19.4MiB live, 407.9MiB allocated

Rules

6 334×	`lower-*.f32`
6 302×	`lower-*.f64`
5 080×	`lower-fma.f32`
5 066×	`lower-fma.f64`
3 274×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	366
0	110	346
1	411	343
2	3341	339
0	9602	328

Stop Event

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

Counts

28 → 461

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (neg.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64)))))))))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (neg.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (neg.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64) (.f64 (.f64 (sin.f64 (neg.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (.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))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #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)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (neg.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))
eps
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.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 eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 eps eps) eps)
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) 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 eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
(+.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x)))
(fma.f64 eps #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) eps x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x x)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (neg.f64 (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))) (neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x x))))
(pow.f64 (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x x))))
(.f64 (.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (/.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)))
(neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
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(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (+.f64 x (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (-.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (fma.f64 eps #s(literal -1/2 binary64) x)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) #s(literal 0 binary64))
(-.f64 (*.f64 eps eps) #s(literal 0 binary64))
(fma.f64 eps eps #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 eps (*.f64 eps eps)) eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 0 binary64)) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 eps eps))
(/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal 0 binary64)) (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 0 binary64)) (.f64 eps eps))
(/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 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))
(-.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 (neg.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))

eval143.0ms (1%)

Memory: 9.6MiB live, 241.0MiB allocated
Compiler: Compiled 31 361 to 2 679 computations (91.5% saved)

prune129.0ms (0.9%)

Memory

-11.4MiB live, 238.1MiB allocated

Pruning

20 alts after pruning (14 fresh and 6 done)

	Pruned	Kept	Total
New	1 163	8	1 171
Fresh	1	6	7
Picked	3	2	5
Done	0	4	4
Total	1 167	20	1 187

Accuracy

100.0%

Counts

1 187 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
	99.7%	(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
✓	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	59.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
	99.9%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.8%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
✓	99.5%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (neg.f64 x)))))) #s(literal 2 binary64))
	99.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
✓	99.5%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
	99.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
	98.6%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))
✓	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
	100.0%	#s(approx (* (* (sin (* (+ eps 0) 1/2)) (+ (* (+ (cos (+ (* 1/2 eps) x)) (cos (+ x (* eps -1/2)))) 1/2) (* (sin (* 1/2 eps)) (sin (neg x))))) 2) (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Compiler

Compiled 971 to 362 computations (62.7% saved)

regimes35.0ms (0.2%)

Memory

14.6MiB live, 52.0MiB allocated

Counts

38 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

12.0ms	eps
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

7.6MiB live, 46.7MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

-29.5MiB live, 45.0MiB allocated

Counts

32 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Memory

1.4MiB live, 38.5MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

30.5MiB live, 30.5MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

-12.3MiB live, 27.0MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

-13.8MiB live, 23.7MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-3.0MiB live, 31.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`
98.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

-21.1MiB live, 14.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	eps
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.3%	1	`x`
5.3%	1	`eps`
5.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify19.0ms (0.1%)

Memory

-23.3MiB live, 19.6MiB allocated

Algorithm

1×	egg-herbie

Rules

62×	`*-commutative_binary64`
8×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`+-rgt-identity_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	365
1	175	365
2	177	365
3	178	365

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (10.8%)

Memory

23.3MiB live, 1 143.5MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
15 160×	`lower-fma.f64`
15 160×	`lower-fma.f32`
14 146×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	155
0	68	131
1	228	131
2	1741	131
0	9666	131
0	433	5880
1	1346	5580
2	3925	5371
0	8108	5041
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	536	5826
1	1728	5587
2	5274	5494
0	8211	5043
0	62	366
0	103	339
1	324	266
2	2686	266
0	8856	257
0	434	3851
1	1275	3670
2	3532	3575
0	8501	3312

Stop Event

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

Compiler

Compiled 619 to 341 computations (44.9% saved)

preprocess139.0ms (1%)

Memory: 9.7MiB live, 202.9MiB allocated
Compiler: Compiled 490 to 218 computations (55.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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%)

analyze40.0ms (0.3%)

sample5.8s (40.7%)

explain97.0ms (0.7%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize26.0ms (0.2%)

series6.0ms (0%)

simplify391.0ms (2.8%)

rewrite313.0ms (2.2%)

eval48.0ms (0.3%)

prune51.0ms (0.4%)

simplify610.0ms (4.3%)

localize254.0ms (1.8%)

series29.0ms (0.2%)

simplify509.0ms (3.6%)

rewrite568.0ms (4%)

eval253.0ms (1.8%)

prune157.0ms (1.1%)

simplify301.0ms (2.1%)

localize273.0ms (1.9%)

series25.0ms (0.2%)

simplify396.0ms (2.8%)

rewrite351.0ms (2.5%)

eval142.0ms (1%)

prune106.0ms (0.8%)

simplify330.0ms (2.3%)

localize217.0ms (1.5%)

series33.0ms (0.2%)

simplify327.0ms (2.3%)

rewrite332.0ms (2.3%)

eval143.0ms (1%)

prune129.0ms (0.9%)

regimes35.0ms (0.2%)

regimes33.0ms (0.2%)

regimes33.0ms (0.2%)

regimes25.0ms (0.2%)

regimes18.0ms (0.1%)

regimes24.0ms (0.2%)

regimes16.0ms (0.1%)

regimes11.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify19.0ms (0.1%)

soundness1.5s (10.8%)

preprocess139.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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