Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze52.0ms (0.3%)

Memory

2.9MiB live, 40.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.6s (60.5%)

Memory

-49.4MiB live, 8 687.0MiB allocated

Samples

4.2s	26 142×	0	invalid
3.1s	5 642×	2	valid
555.0ms	2 481×	1	valid
17.0ms	133×	0	valid

Precisions

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

ival-cos: 2.6s (43.7% of total)

const: 778.0ms (12.9% of total)

ival-sub: 506.0ms (8.4% of total)

adjust: 417.0ms (6.9% of total)

ival-<: 359.0ms (5.9% of total)

ival-mult: 305.0ms (5.1% of total)

ival-<=: 301.0ms (5% of total)

ival-add: 283.0ms (4.7% of total)

ival-fabs: 278.0ms (4.6% of total)

ival-and: 109.0ms (1.8% of total)

exact: 50.0ms (0.8% of total)

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

Bogosity

explain452.0ms (2.9%)

Memory

1.9MiB live, 396.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
130	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	130	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	130	0
-	0	126

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	0
-	0	0	126

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	126
1	129
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

333.0ms	354×	2	valid
20.0ms	152×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 303.0ms

ival-cos: 272.0ms (89.8% of total)

adjust: 20.0ms (6.6% of total)

ival-sub: 7.0ms (2.3% of total)

ival-add: 4.0ms (1.3% of total)

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

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

preprocess24.0ms (0.2%)

Memory

28.8MiB live, 28.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize192.0ms (1.2%)

Memory

-43.3MiB live, 46.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.05424472348973429	(cos.f64 (+.f64 x eps))
accuracy	29.05936511403581	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

175.0ms	177×	2	valid
10.0ms	76×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-cos: 50.0ms (54.5% of total)

ival-add: 29.0ms (31.6% of total)

adjust: 9.0ms (9.8% of total)

ival-sub: 3.0ms (3.3% of total)

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

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

series4.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Counts

4 → 33

Calls

Call 1

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

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

Calls

6 calls:

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

simplify242.0ms (1.5%)

Memory

28.7MiB live, 104.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	277	293
2	628	293
3	2426	292
0	8397	272

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite301.0ms (1.9%)

Memory

-2.1MiB live, 118.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	385	16
3	4790	16
0	8343	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (-.f64 (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64))))
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(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (-.f64 eps x)) (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))))
(fma.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))) (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))) (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(cos.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(cos.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(cos.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))) (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(exp.f64 (*.f64 (log.f64 (cos.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))

eval65.0ms (0.4%)

Memory: -11.9MiB live, 26.1MiB allocated
Compiler: Compiled 6 613 to 893 computations (86.5% saved)

prune9.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	242	9	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	243	9	252

Accuracy

99.8%

Counts

252 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	54.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	53.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
▶	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))

Compiler

Compiled 302 to 226 computations (25.2% saved)

simplify343.0ms (2.2%)

Memory

8.7MiB live, 128.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	233
0	69	223
1	119	223
2	231	219
3	393	219
4	822	219
5	1604	219
6	1978	219
7	2457	219
8	2990	219
9	3979	219
10	5343	219
11	6306	219
12	6590	219
13	6664	219
14	6691	219
15	7034	219
16	7219	219
17	7292	219
18	7302	219
19	7302	219
20	7302	219
0	8128	215

Stop Event

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

Calls

Call 1

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

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

localize459.0ms (2.9%)

Memory

-19.2MiB live, 278.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x))
accuracy	0.015625	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.1484375	(.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)
accuracy	0.1487207747502838	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
accuracy	0.0	(*.f64 x x)
accuracy	0.05424472348973429	(cos.f64 (+.f64 x eps))
accuracy	0.39108328553694827	#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	29.05936511403581	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(neg.f64 (sin.f64 x))
accuracy	0.01171875	(*.f64 (neg.f64 (sin.f64 x)) eps)
accuracy	12.451302989470824	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
accuracy	0.0	(cos.f64 eps)
accuracy	29.024389660684626	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	29.1659169035305	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.03125	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.15234375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

307.0ms	180×	2	valid
40.0ms	75×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 429 to 79 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 275.0ms

ival-cos: 105.0ms (38.1% of total)

adjust: 72.0ms (26.1% of total)

ival-neg: 38.0ms (13.8% of total)

ival-mult: 32.0ms (11.6% of total)

ival-sub: 10.0ms (3.6% of total)

ival-sin: 7.0ms (2.5% of total)

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

const: 4.0ms (1.5% of total)

exact: 1.0ms (0.4% of total)

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

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

series64.0ms (0.4%)

Memory

2.8MiB live, 38.4MiB allocated

Counts

22 → 110

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
43.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* x x))
6.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* x x))
4.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* x x))
4.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* x x))
3.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* x x))

simplify166.0ms (1%)

Memory

-0.7MiB live, 158.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	381	1418
1	1147	1367
2	3049	1321
3	7010	1321
0	8101	1203

Stop Event

1×	iter limit
1×	node limit

Counts

110 → 108

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 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))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
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)))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(pow x 2)
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(sin x)
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(sin (* 1/2 (+ eps (* 2 x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin (* 1/2 (- eps (* -2 x))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (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 x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(sin (* 1/2 (- (* 2 x) (* -1 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)
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 (neg.f64 x) eps))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(sin x)
(sin.f64 x)
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(fma.f64 (/.f64 eps x) x x)
(cos x)
(cos.f64 x)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(- (* -1/2 (* eps (cos x))) (sin x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite218.0ms (1.4%)

Memory

-8.5MiB live, 149.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	181
0	69	173
1	242	173
2	1834	173
0	8857	173

Stop Event

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

Counts

22 → 490

Calls

Call 1

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

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

eval86.0ms (0.5%)

Memory: 18.0MiB live, 94.4MiB allocated
Compiler: Compiled 18 257 to 2 484 computations (86.4% saved)

prune61.0ms (0.4%)

Memory

-35.8MiB live, 48.0MiB allocated

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	574	21	595
Fresh	2	2	4
Picked	4	1	5
Done	0	0	0
Total	580	24	604

Accuracy

100.0%

Counts

604 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.7%	(.f64 (.f64 (sin.f64 (-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	85.0%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	53.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	84.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps)))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
✓	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
▶	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
▶	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
▶	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
	99.3%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))

Compiler

Compiled 1 287 to 890 computations (30.8% saved)

simplify159.0ms (1%)

Memory

30.7MiB live, 107.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	438
0	95	434
1	167	434
2	373	428
3	844	424
4	2525	424
5	4847	424
6	7168	424
0	8074	424

Stop Event

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

Calls

Call 1

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

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
eps
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
#s(approx (neg (sin x)) (neg.f64 x))
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))) eps))
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps)
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))) eps)
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))
(fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
eps
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))
#s(literal 1/4 binary64)
(*.f64 x x)
x
#s(literal -1/2 binary64)
(neg.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
(.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x))
#s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(cos.f64 x)
#s(literal -1/2 binary64)

localize508.0ms (3.2%)

Memory

5.8MiB live, 325.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
accuracy	0.015625	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.027164829337448734	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
accuracy	0.15234375	(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
accuracy	0.01171875	(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
accuracy	0.3066077991683265	#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x))
accuracy	12.451302989470824	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
accuracy	0.0	(neg.f64 x)
accuracy	0.1484375	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps)
accuracy	0.1487207747502838	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
accuracy	0.9713414923865996	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))
accuracy	0.0	(neg.f64 x)
accuracy	0.01171875	(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
accuracy	0.9635289925211264	#s(approx (neg (sin x)) (neg.f64 x))
accuracy	12.451302989470824	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
accuracy	0.0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.015625	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.03125	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.15234375	(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))

Samples

352.0ms	174×	2	valid
107.0ms	78×	1	valid
2.0ms	4×	0	valid

Compiler

Compiled 735 to 122 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 406.0ms

ival-mult: 169.0ms (41.6% of total)

adjust: 113.0ms (27.8% of total)

ival-cos: 53.0ms (13% of total)

ival-add: 35.0ms (8.6% of total)

const: 16.0ms (3.9% of total)

ival-sin: 10.0ms (2.5% of total)

ival-sub: 7.0ms (1.7% of total)

ival-neg: 3.0ms (0.7% of total)

exact: 1.0ms (0.2% of total)

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

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

series32.0ms (0.2%)

Memory

-33.0MiB live, 12.0MiB allocated

Counts

22 → 117

Calls

Call 1

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

Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 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))))
1/6
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(sin (+ x (* 1/2 eps)))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* 1/5040 (pow x 4))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* -1/2 (* eps (cos x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(sin (- (* 1/2 eps) (* -1 x)))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(sin (- x (* -1/2 eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	x	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* (* (cos x) -1/2) eps))
4.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* (* (cos x) -1/2) eps))
3.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* (* (cos x) -1/2) eps))
3.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* (* (cos x) -1/2) eps))
3.0ms	eps	@	0	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* (* (cos x) -1/2) eps))

simplify175.0ms (1.1%)

Memory

26.6MiB live, 64.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	421	1740
1	1283	1676
2	3695	1615
0	8253	1492

Stop Event

1×	iter limit
1×	node limit

Counts

117 → 116

Calls

Call 1

Inputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 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))))
1/6
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(sin (+ x (* 1/2 eps)))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* 1/5040 (pow x 4))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* -1/2 (* eps (cos x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(sin (- (* 1/2 eps) (* -1 x)))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(sin (- x (* -1/2 eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))

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

rewrite174.0ms (1.1%)

Memory

-4.6MiB live, 151.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	355
0	95	351
1	351	351
2	2887	351
0	8224	349

Stop Event

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

Counts

22 → 388

Calls

Call 1

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

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

eval58.0ms (0.4%)

Memory: 2.6MiB live, 79.1MiB allocated
Compiler: Compiled 22 299 to 2 473 computations (88.9% saved)

prune43.0ms (0.3%)

Memory

-9.8MiB live, 37.1MiB allocated

Pruning

29 alts after pruning (23 fresh and 6 done)

	Pruned	Kept	Total
New	480	12	492
Fresh	7	11	18
Picked	0	5	5
Done	0	1	1
Total	487	29	516

Accuracy

100.0%

Counts

516 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	85.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	83.8%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) (neg.f64 eps)))
	72.0%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (neg (sin x)) (neg.f64 x))) (neg.f64 eps)))
	53.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
✓	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
✓	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	34.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 (.f64 eps eps))))) (.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))) eps))
▶	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
▶	47.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x) x))) eps))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
▶	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x))) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Compiler

Compiled 1 674 to 1 122 computations (33% saved)

simplify129.0ms (0.8%)

Memory

-3.5MiB live, 111.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	617
0	103	607
1	189	607
2	438	603
3	932	603
4	2590	603
5	7300	578
0	8327	558

Stop Event

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

Calls

Call 1

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

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

localize334.0ms (2.1%)

Memory

24.5MiB live, 304.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1487207747502838	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
accuracy	0.9713414923865996	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))))
accuracy	29.38217285070722	(.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))
accuracy	31.032554995056827	(fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))
accuracy	0.1487207747502838	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy	0.213222509768442	(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
accuracy	0.32421875	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.4609240282303106	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.0078125	(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
accuracy	0.027164829337448734	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy	0.1484375	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.9635054687468964	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) eps)
accuracy	0.14453125	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy	0.1487207747502838	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
accuracy	58.68790326547614	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.03125	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1484375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)))
accuracy	0.3125	(*.f64 #s(literal -1/48 binary64) eps)

Samples

221.0ms	172×	2	valid
61.0ms	78×	1	valid
4.0ms	2×	5	exit
2.0ms	4×	0	valid

Compiler

Compiled 977 to 137 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-mult: 73.0ms (31.1% of total)

ival-cos: 53.0ms (22.6% of total)

adjust: 48.0ms (20.5% of total)

ival-add: 25.0ms (10.7% of total)

const: 10.0ms (4.3% of total)

ival-sub: 8.0ms (3.4% of total)

ival-div: 7.0ms (3% of total)

ival-sin: 7.0ms (3% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series30.0ms (0.2%)

Memory

-7.1MiB live, 30.8MiB allocated

Counts

24 → 134

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (* (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/48 eps) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)))
6.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (* (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/48 eps) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)))
4.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (* (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/48 eps) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)))
4.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (* (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/48 eps) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)))
4.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (* (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (* x x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/48 eps) (* 1/6 x) (+ (* 1/4 eps) (* 1/6 x)) (+ (* eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)))

simplify155.0ms (1%)

Memory

-17.7MiB live, 137.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	425	1876
1	1322	1792
2	3903	1741
0	8493	1609

Stop Event

1×	iter limit
1×	node limit

Counts

134 → 133

Calls

Call 1

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

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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 x #s(literal -2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) x) #s(literal 1 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)) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(fma.f64 (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)) #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/4 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/4 eps)
(*.f64 #s(literal 1/4 binary64) eps)
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(/ (+ (* -1 x) (* -1/2 eps)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) x) x)
(/ (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/4 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(- (* -1/2 (* eps (cos x))) (sin x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(* x (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) x)
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(*.f64 (+.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/2 binary64) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/4 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) eps)
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (.f64 x x))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)) x)
(- (* 1/4 eps) (/ 1 x))
(fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x))
(- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))
(fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) eps (/.f64 #s(literal -1 binary64) x))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) x)
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 eps x) #s(literal -1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
(*.f64 (neg.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x) x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(*.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 eps x) #s(literal -1/6 binary64)) (neg.f64 x))
(+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))
(fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x)))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(* x (- (* 1/6 (pow x 2)) 1))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(+ (* -1 x) (* eps (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))))
(fma.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (*.f64 x x) (neg.f64 x))
(* -1/48 eps)
(*.f64 #s(literal -1/48 binary64) eps)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(- (* eps (- 1/4 (* 1/2 (/ 1 (pow x 2))))) (/ 1 x))
(fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) eps (/.f64 #s(literal -1 binary64) x))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(* -1/2 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(* 1/6 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) x)
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) eps) eps)
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (.f64 eps eps))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps)
(* eps (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (.f64 x x))
(* eps (+ (* -1 (/ x eps)) (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))))
(.f64 (.f64 x (fma.f64 x (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) eps))) eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps)
(* eps (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps)
(* eps (- 1/4 (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 (* eps x)))))
(fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) eps (/.f64 #s(literal -1 binary64) x))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) eps) eps)
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps)
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(.f64 (fma.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal 1/2 binary64)) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))) (/ x eps))))
(.f64 (.f64 x (fma.f64 x (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) eps))) eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (- 1/4 (* 1/2 (/ 1 (pow x 2))))) (/ 1 (* eps x)))))
(fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) eps (/.f64 #s(literal -1 binary64) x))

rewrite187.0ms (1.2%)

Memory

-4.2MiB live, 158.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	489
0	103	482
1	403	482
2	3527	482
0	10173	467

Stop Event

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

Counts

24 → 237

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.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 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #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 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)))
(fma.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
(sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
(.f64 eps #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))
(/.f64 (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(fma.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 0 binary64) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(fma.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) eps (.f64 #s(literal 0 binary64) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) eps (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(fma.f64 eps #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 #s(literal 0 binary64) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 eps #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps))) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(+.f64 (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 0 binary64)) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(+.f64 (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) eps) (.f64 #s(literal 0 binary64) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))))
(+.f64 (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (.f64 #s(literal -1/2 binary64) eps)) eps) (.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 0 binary64)))
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
(*.f64 eps #s(literal -1/2 binary64))
(/.f64 (.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/2 binary64)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))
(fma.f64 #s(literal -1/2 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/2 binary64) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64))) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (.f64 x (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 eps #s(literal 1/2 binary64))) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64))) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)))))
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(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
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(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x))))
(+.f64 (.f64 #s(literal 1/4 binary64) eps) (.f64 #s(literal 1/6 binary64) x))
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(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
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(pow.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64))
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(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps)))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64)))))
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(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (pow.f64 x #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal -2 binary64)) eps) (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)))
(fma.f64 eps (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps (pow.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (fma.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps (pow.f64 x #s(literal -1 binary64)))))
(+.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)) (*.f64 #s(literal 1/4 binary64) eps))
(+.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) eps) (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)))
(+.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps) (/.f64 #s(literal -1 binary64) x))
(+.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) eps))

eval58.0ms (0.4%)

Memory: 22.0MiB live, 67.8MiB allocated
Compiler: Compiled 17 011 to 1 859 computations (89.1% saved)

prune30.0ms (0.2%)

Memory

-30.3MiB live, 48.0MiB allocated

Pruning

31 alts after pruning (23 fresh and 8 done)

	Pruned	Kept	Total
New	360	8	368
Fresh	3	15	18
Picked	3	2	5
Done	0	6	6
Total	366	31	397

Accuracy

100.0%

Counts

397 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	85.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	83.8%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) (neg.f64 eps)))
	72.0%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (neg (sin x)) (neg.f64 x))) (neg.f64 eps)))
	53.4%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
✓	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
✓	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	34.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 (.f64 eps eps))))) (.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))) eps))
✓	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(approx (+ ( eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) x))) eps))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (.f64 eps eps)))) eps))
	95.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) eps) eps))) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Compiler

Compiled 2 703 to 1 080 computations (60% saved)

regimes36.0ms (0.2%)

Memory

3.7MiB live, 43.1MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(approx (+ ( eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (neg (sin x)) (neg.f64 x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) eps) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 (.f64 eps eps))))) (.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps)))
(.f64 (.f64 (sin.f64 (-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

34.2MiB live, 34.2MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(approx (+ ( eps (+ (/ -1/2 (* x x)) 1/4)) (/ -1 x)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (neg (sin x)) (neg.f64 x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)) eps) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 (fma.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 (.f64 eps eps))))) (.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.2%)

Memory

-12.9MiB live, 29.6MiB allocated

Counts

34 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.2%)

Memory

5.9MiB live, 45.4MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.1%)

Memory

-7.4MiB live, 31.9MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

-20.5MiB live, 19.1MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

6.8MiB live, 6.8MiB allocated

Accuracy

Total -16.4b remaining (-128.5%)

Threshold costs -16.4b (-128.5%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
80.0%	1	`x`
80.0%	1	`eps`
80.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify168.0ms (1.1%)

Memory

-25.8MiB live, 55.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	303
1	150	303
2	273	301
3	548	299
4	1028	299
5	1580	299
6	2300	299
7	3135	299
8	3466	299
9	3629	299
10	3721	299
11	3776	299
12	3834	299
13	4386	299
14	4762	299
15	5067	299
16	5411	299
17	6022	299
18	7156	299

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness1.0s (6.5%)

Memory

26.5MiB live, 220.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	425	1876
1	1322	1792
2	3903	1741
0	8493	1609
0	6	16
0	10	16
1	54	16
2	385	16
3	4790	16
0	8343	16
0	381	1418
1	1147	1367
2	3049	1321
3	7010	1321
0	8101	1203
0	105	296
1	277	293
2	628	293
3	2426	292
0	8397	272
0	421	1740
1	1283	1676
2	3695	1615
0	8253	1492

Stop Event

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

Compiler

Compiled 423 to 219 computations (48.2% saved)

preprocess83.0ms (0.5%)

Memory: -4.2MiB live, 35.3MiB allocated
Compiler: Compiled 662 to 250 computations (62.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

start0.0ms (0%)

analyze52.0ms (0.3%)

sample9.6s (60.5%)

explain452.0ms (2.9%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize192.0ms (1.2%)

series4.0ms (0%)

simplify242.0ms (1.5%)

rewrite301.0ms (1.9%)

eval65.0ms (0.4%)

prune9.0ms (0.1%)

simplify343.0ms (2.2%)

localize459.0ms (2.9%)

series64.0ms (0.4%)

simplify166.0ms (1%)

rewrite218.0ms (1.4%)

eval86.0ms (0.5%)

prune61.0ms (0.4%)

simplify159.0ms (1%)

localize508.0ms (3.2%)

series32.0ms (0.2%)

simplify175.0ms (1.1%)

rewrite174.0ms (1.1%)

eval58.0ms (0.4%)

prune43.0ms (0.3%)

simplify129.0ms (0.8%)

localize334.0ms (2.1%)

series30.0ms (0.2%)

simplify155.0ms (1%)

rewrite187.0ms (1.2%)

eval58.0ms (0.4%)

prune30.0ms (0.2%)

regimes36.0ms (0.2%)

regimes28.0ms (0.2%)

regimes26.0ms (0.2%)

regimes24.0ms (0.2%)

regimes20.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify168.0ms (1.1%)

soundness1.0s (6.5%)

preprocess83.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18