Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze63.0ms (0.4%)

Memory

-29.3MiB live, 109.5MiB 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 (63.5%)

Memory

25.5MiB live, 8 976.2MiB allocated

Samples

3.8s	5 718×	2	valid
3.3s	26 158×	0	invalid
518.0ms	2 435×	1	valid
13.0ms	103×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-cos: 3.1s (51.4% of total)

const: 701.0ms (11.5% of total)

adjust: 417.0ms (6.9% of total)

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

ival-sub: 306.0ms (5% of total)

ival-mult: 284.0ms (4.7% of total)

ival-<=: 270.0ms (4.4% of total)

ival-<: 256.0ms (4.2% of total)

ival-fabs: 197.0ms (3.2% of total)

ival-and: 104.0ms (1.7% of total)

exact: 47.0ms (0.8% of total)

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

Bogosity

explain269.0ms (1.8%)

Memory

-1.3MiB live, 197.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
128	1	(-9.96688420981063e-158 1.9277751581046517e-166)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	129	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	128	0
-	1	127

Precision

0.9922480620155039

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	1	0	127

Precision?

0.9922480620155039

Recall?

1.0

Freqs

test

number	freq
0	127
1	128
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

206.0ms	354×	2	valid
19.0ms	154×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-cos: 120.0ms (81% of total)

adjust: 18.0ms (12.2% of total)

ival-sub: 6.0ms (4.1% of total)

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

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

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

preprocess50.0ms (0.3%)

Memory

-28.4MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	46	41
2	86	41
3	116	41
4	118	41
0	6	7
0	10	7
1	22	7
2	40	7
3	64	7
4	71	7
0	71	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
▶	54.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Memory

4.0MiB live, 4.0MiB 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	22	18
2	40	18
3	64	18
4	71	18
0	71	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)

localize110.0ms (0.7%)

Memory

22.6MiB live, 123.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.04237131775816928	(cos.f64 (+.f64 x eps))
accuracy	29.25275467006105	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

93.0ms	177×	2	valid
10.0ms	77×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-cos: 55.0ms (78.6% of total)

adjust: 10.0ms (14.3% of total)

ival-sub: 3.0ms (4.3% of total)

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

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

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

series20.0ms (0.1%)

Memory

-37.1MiB live, 8.2MiB 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
17.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	inf	((- (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))

simplify131.0ms (0.9%)

Memory

9.5MiB live, 102.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	308	293
2	779	293
3	2454	292
4	6244	292
0	8035	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)
(-.f64 (cos.f64 eps) (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (cos.f64 eps) #s(literal -1/2 binary64)) (sin.f64 eps)) x #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) (cos.f64 eps)) x (sin.f64 eps)) (neg.f64 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 (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (.f64 #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 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 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 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 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 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 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)

rewrite171.0ms (1.1%)

Memory

29.2MiB live, 125.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	62	16
2	615	16
0	8130	16

Stop Event

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

Counts

4 → 138

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

eval31.0ms (0.2%)

Memory: -10.1MiB live, 35.5MiB allocated
Compiler: Compiled 4 780 to 715 computations (85% saved)

prune6.0ms (0%)

Memory

16.1MiB live, 16.1MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	7	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	154	8	162

Accuracy

99.8%

Counts

162 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	53.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	83.5%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	53.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.6%	#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)))
▶	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 219 to 166 computations (24.2% saved)

simplify147.0ms (1%)

Memory

-11.9MiB live, 131.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	161
0	47	161
1	82	161
2	163	161
3	361	161
4	641	161
5	1015	161
6	1741	161
7	3335	161
8	6054	161
0	8297	161

Stop Event

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

Calls

Call 1

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

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

localize365.0ms (2.4%)

Memory

-25.9MiB live, 260.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.04237131775816928	(cos.f64 (+.f64 x eps))
accuracy	0.49211070361754117	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	29.25275467006105	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(neg.f64 eps)
accuracy	0.0078125	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	13.468080241331913	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0.0	(+.f64 x eps)
accuracy	0.04237131775816928	(cos.f64 (+.f64 x eps))
accuracy	0.6749212382856904	#s(approx (cos x) #s(literal 1 binary64))
accuracy	29.25275467006105	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.0	(cos.f64 eps)
accuracy	28.741970280184113	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	28.953410913321463	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
accuracy	0.12126844999722695	#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)))
accuracy	0.13671875	(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))

Samples

234.0ms	181×	2	valid
25.0ms	74×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 125 to 23 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 194.0ms

ival-cos: 95.0ms (48.9% of total)

adjust: 64.0ms (33% of total)

ival-mult: 18.0ms (9.3% of total)

ival-sub: 7.0ms (3.6% of total)

ival-add: 6.0ms (3.1% of total)

ival-sin: 3.0ms (1.5% of total)

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

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.1%)

Memory

27.4MiB live, 27.4MiB allocated

Counts

18 → 69

Calls

Call 1

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

Calls

6 calls:

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

simplify225.0ms (1.5%)

Memory

-8.9MiB live, 174.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	226	742
1	760	733
2	2444	711
3	5009	711
0	8441	659

Stop Event

1×	iter limit
1×	node limit

Counts

69 → 67

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)
(* -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)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(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 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 (* 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)))))))))
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))))
(pow x 2)
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -1 (* eps (sin x)))
(sin x)
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos 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))))
(* -1 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 (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* eps (+ 1 (/ x eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (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 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (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)))
(* -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)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 (.f64 x x) eps) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
(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 (-.f64 (.f64 (.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 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 (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #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 #s(literal 1/6 binary64) x) x #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 (.f64 x x) #s(literal -1/120 binary64) #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 (.f64 #s(literal 1/5040 binary64) x) x #s(literal -1/120 binary64))) (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) 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)) (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(pow x 2)
(*.f64 x x)
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(cos x)
(cos.f64 x)
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(sin x)
(sin.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 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) 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 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #s(literal 1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #s(literal 1/2 binary64))) (.f64 eps eps))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #s(literal 1/2 binary64))) (.f64 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 (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #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 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) 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 (neg.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(* -1 eps)
(neg.f64 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 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* 1/2 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (-.f64 (/.f64 x (neg.f64 eps)) #s(literal 1 binary64)) (neg.f64 eps))

rewrite213.0ms (1.4%)

Memory

-52.0MiB live, 229.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	128
0	47	128
1	175	128
2	1413	128
0	8759	128

Stop Event

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

Counts

18 → 179

Calls

Call 1

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

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

eval49.0ms (0.3%)

Memory: 19.8MiB live, 110.0MiB allocated
Compiler: Compiled 7 845 to 1 045 computations (86.7% saved)

prune11.0ms (0.1%)

Memory

31.0MiB live, 31.0MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	302	8	310
Fresh	0	2	2
Picked	3	2	5
Done	0	1	1
Total	305	13	318

Accuracy

100.0%

Counts

318 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	83.5%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))))
✓	99.6%	#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)))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
✓	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg 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) eps) 1/2) (sin x)) (neg 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))))
▶	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
▶	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 575 to 394 computations (31.5% saved)

simplify136.0ms (0.9%)

Memory

-6.1MiB live, 187.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	404
0	85	400
1	171	399
2	422	397
3	1187	397
4	2554	397
5	4116	397
6	5556	397
7	7568	397
0	8114	394

Stop Event

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

Calls

Call 1

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

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

localize334.0ms (2.2%)

Memory

-29.5MiB live, 444.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 #s(approx (* (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64) (sin.f64 x))
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
accuracy	0.13671875	(.f64 (fma.f64 #s(approx ( (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
accuracy	0.4917045500748083	#s(approx (* (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
accuracy	0.13671875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
accuracy	0.32421875	(fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps))
accuracy	0.47095088605790125	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.0078125	(.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)
accuracy	0.3671875	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.47178088857792155	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
accuracy	13.278142806084052	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
accuracy	0.0	(*.f64 (neg.f64 x) eps)
accuracy	0.0	(neg.f64 x)
accuracy	0.6510317728384727	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	13.278142806084052	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.0078125	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))
accuracy	0.015625	(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps)))
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))))

Samples

239.0ms	171×	2	valid
48.0ms	81×	1	valid
3.0ms	2×	5	exit
1.0ms	2×	0	valid

Compiler

Compiled 255 to 45 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 240.0ms

ival-mult: 79.0ms (33% of total)

ival-cos: 78.0ms (32.5% of total)

adjust: 46.0ms (19.2% of total)

ival-add: 16.0ms (6.7% of total)

const: 11.0ms (4.6% of total)

ival-sub: 3.0ms (1.3% of total)

ival-sin: 3.0ms (1.3% of total)

ival-neg: 2.0ms (0.8% of total)

exact: 1.0ms (0.4% of total)

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

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

series26.0ms (0.2%)

Memory

31.1MiB live, 31.1MiB allocated

Counts

23 → 75

Calls

Call 1

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

Outputs
(* -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 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 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)
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 (* 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)
(* -1 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* 1/6 x)
(* -1/4 eps)
(+ (* -1/4 eps) (* -1/6 x))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(- (cos (+ eps x)) (cos x))
(sin x)
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))
(* eps (cos x))
(* -1/6 x)
(* x (- (* -1/4 (/ eps x)) 1/6))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))
(* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos 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)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/6 (pow x 2)) 1))
(+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))
(* eps (- (* -1/6 (/ x eps)) 1/4))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* (* 1/2 (* (cos x) eps)) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (* eps (+ (* (* 1/6 x) x) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* (cos x) eps) (* 1/6 x) (+ (* -1/6 x) (* -1/4 eps)))
4.0ms	eps	@	0	((+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* (* 1/2 (* (cos x) eps)) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (* eps (+ (* (* 1/6 x) x) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* (cos x) eps) (* 1/6 x) (+ (* -1/6 x) (* -1/4 eps)))
4.0ms	eps	@	inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* (* 1/2 (* (cos x) eps)) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (* eps (+ (* (* 1/6 x) x) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* (cos x) eps) (* 1/6 x) (+ (* -1/6 x) (* -1/4 eps)))
4.0ms	eps	@	-inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* (* 1/2 (* (cos x) eps)) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (* eps (+ (* (* 1/6 x) x) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* (cos x) eps) (* 1/6 x) (+ (* -1/6 x) (* -1/4 eps)))
3.0ms	x	@	-inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* (* 1/2 (* (cos x) eps)) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (* eps (+ (* (* 1/6 x) x) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* (cos x) eps) (* 1/6 x) (+ (* -1/6 x) (* -1/4 eps)))

simplify236.0ms (1.6%)

Memory

-11.2MiB live, 126.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	268	916
1	922	880
2	3420	829
0	8311	771

Stop Event

1×	iter limit
1×	node limit

Counts

75 → 73

Calls

Call 1

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

Outputs
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) eps))
(+ (* -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 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(fma.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) x) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 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 (.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)))
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)) (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(*.f64 eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 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 (.f64 x x) #s(literal -1/120 binary64) #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 (.f64 #s(literal 1/5040 binary64) x) x #s(literal -1/120 binary64))) (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* -1 eps)
(neg.f64 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x)
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 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
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* -1/4 eps)
(*.f64 #s(literal -1/4 binary64) eps)
(+ (* -1/4 eps) (* -1/6 x))
(fma.f64 #s(literal -1/4 binary64) eps (*.f64 #s(literal -1/6 binary64) x))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(sin x)
(sin.f64 x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* 1/6 (* eps (pow x 3)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64)) eps)
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) eps (/.f64 eps (.f64 x x))))
(* 1/6 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (.f64 eps (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1/6 binary64))) (*.f64 x x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(* -1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))
(.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/4 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))
(*.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) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (-.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)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* -1/6 x)
(*.f64 #s(literal -1/6 binary64) x)
(* x (- (* -1/4 (/ eps x)) 1/6))
(.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/4 binary64)) #s(literal 1/6 binary64)) x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) eps (/.f64 eps (.f64 x x))))
(* -1 (* (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)))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))
(*.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)))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))
(*.f64 (+.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (/.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)))
(* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)) x)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) 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 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
(+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))
(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))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps) eps)
(* 1/2 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))
(.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps)
(* eps (- (* -1/6 (/ x eps)) 1/4))
(.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/6 binary64)) #s(literal 1/4 binary64)) eps)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* 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)) eps)
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (neg.f64 eps))
(* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))
(.f64 (-.f64 (.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps))) #s(literal 1/2 binary64)) (neg.f64 eps))
(* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) eps)

rewrite338.0ms (2.2%)

Memory

7.9MiB live, 145.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	330
0	85	326
1	306	325
2	2246	325
0	8208	320

Stop Event

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

Counts

23 → 199

Calls

Call 1

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

Outputs
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))) (.f64 (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)))) (.f64 (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64))) (.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 3 binary64)))) (.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (.f64 (neg.f64 eps) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 eps) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (neg.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)) (.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)))) (neg.f64 (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) eps) #s(literal 3 binary64))) #s(literal 1/8 binary64) (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64))) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (neg.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) eps) #s(literal 3 binary64))) #s(literal 1/8 binary64) (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps)))))
(/.f64 (fma.f64 (neg.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) eps) #s(literal 3 binary64))) #s(literal 1/8 binary64) (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64))))
(neg.f64 (fma.f64 eps (sin.f64 x) (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps)))
(neg.f64 (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps (*.f64 eps (sin.f64 x))))
(neg.f64 (.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 (neg.f64 eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 (neg.f64 eps) (cos.f64 x)) (.f64 #s(literal 1/2 binary64) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 (neg.f64 eps) #s(literal 1/2 binary64)) (.f64 (cos.f64 x) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps)) #s(literal 1/2 binary64) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (neg.f64 eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (neg.f64 eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 x) (.f64 (.f64 #s(literal 1/2 binary64) eps) (neg.f64 eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (neg.f64 eps) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(-.f64 (/.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(-.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps))))
(-.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (neg.f64 eps)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))
(-.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps))
(-.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (neg.f64 eps)))
(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 (neg.f64 eps)) (sin.f64 x)))
(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 eps)))
(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 eps (sin.f64 x)))
(+.f64 (/.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x))) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 2 binary64)))))
(+.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(+.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (neg.f64 eps) (sin.f64 x)))
(.f64 (.f64 (neg.f64 eps) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (.f64 (neg.f64 eps) (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) eps))
(.f64 (.f64 (neg.f64 eps) #s(literal 1/2 binary64)) (*.f64 (cos.f64 x) eps))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) (neg.f64 eps)) #s(literal 1/2 binary64))
(.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (neg.f64 eps)))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps)
(.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (neg.f64 eps))
(.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/2 binary64) (neg.f64 eps)))
(.f64 (cos.f64 x) (.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 eps)))
(.f64 #s(literal 1/2 binary64) (.f64 (*.f64 (cos.f64 x) eps) (neg.f64 eps)))
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(-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal 1/4 binary64) eps))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal 1/6 binary64) x))
(+.f64 (/.f64 (.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))))) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))))))
(+.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))
(+.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))

eval72.0ms (0.5%)

Memory: 31.3MiB live, 64.5MiB allocated
Compiler: Compiled 10 116 to 1 287 computations (87.3% saved)

prune97.0ms (0.6%)

Memory

-32.2MiB live, 75.2MiB allocated

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	265	5	270
Fresh	2	3	5
Picked	2	3	5
Done	0	3	3
Total	269	14	283

Accuracy

100.0%

Counts

283 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	83.5%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) #s(approx (* (* 1/2 (* (cos x) eps)) (neg eps)) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))))
✓	99.6%	#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)))
✓	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
▶	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
	55.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
▶	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) eps))))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 670 to 458 computations (31.6% saved)

simplify199.0ms (1.3%)

Memory

-5.9MiB live, 229.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	606
0	100	596
1	216	582
2	596	565
3	1980	557
4	6119	557
0	8048	542

Stop Event

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

Calls

Call 1

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

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

localize329.0ms (2.2%)

Memory

27.4MiB live, 452.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05187801082082267	(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
accuracy	0.13671875	(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
accuracy	0.29296875	(+.f64 (+.f64 eps x) x)
accuracy	22.856000921245887	(-.f64 (+.f64 eps x) x)
accuracy	0.13671875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps))) (neg.f64 eps))
accuracy	0.25390625	(.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps)
accuracy	0.32421875	(fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64))
accuracy	0.47095088605790125	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps)))
accuracy	0.0	(neg.f64 x)
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) eps))))
accuracy	0.12890625	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) eps))
accuracy	0.6510260875699547	#s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) eps)))
accuracy	0.0	(neg.f64 eps)
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
accuracy	0.13671875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
accuracy	0.6569596975327598	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.0	(neg.f64 eps)
accuracy	0.015625	(fma.f64 (sin.f64 x) (neg.f64 eps) #s(approx (* (* 1/2 (* (cos x) eps)) (neg eps)) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
accuracy	0.12126844999722695	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) #s(approx (* (* 1/2 (* (cos x) eps)) (neg eps)) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))))
accuracy	0.4912886148225708	#s(approx (* (* 1/2 (* (cos x) eps)) (neg eps)) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))

Samples

221.0ms	172×	2	valid
59.0ms	82×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 368 to 60 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 223.0ms

ival-mult: 67.0ms (30.1% of total)

ival-cos: 54.0ms (24.2% of total)

adjust: 49.0ms (22% of total)

ival-add: 26.0ms (11.7% of total)

const: 7.0ms (3.1% of total)

ival-sin: 7.0ms (3.1% of total)

ival-div: 6.0ms (2.7% of total)

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

ival-neg: 2.0ms (0.9% of total)

exact: 1.0ms (0.4% of total)

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

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

series29.0ms (0.2%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

26 → 114

Calls

Call 1

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

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)
(* -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)))))))
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))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* 2 x))
(* -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))))))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(* -1 x)
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (* x (+ (* -1/4 x) (/ 1 eps))))
(+ 1/2 (* x (+ (* x (- (* -1/6 (/ x eps)) 1/4)) (/ 1 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* 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 x)) (cos x))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/6 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))
(* (pow x 3) (- (/ 1 (* eps (pow x 2))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))
(* (pow x 3) (- (+ (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 (pow x 3)))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 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 (- (* -1/2 (/ eps x)) 1)))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (/ 1 (* eps x)) 1/4) x)) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (/ 1/2 (pow x 2)) (/ 1 (* eps x))) 1/4) x)) (* 1/6 (/ 1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 eps)
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(pow eps 2)
(+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))
(* 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)))))))))
(/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)
(/ (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2))))) eps)
(* 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) (* 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))))))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* eps (+ 1/2 (/ x eps)))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (sin x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* 1/2 eps) x) (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* 1/2 (* (cos x) eps)) (neg eps)) (neg x) (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) (* (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
4.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (sin x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* 1/2 eps) x) (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* 1/2 (* (cos x) eps)) (neg eps)) (neg x) (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) (* (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
4.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (sin x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* 1/2 eps) x) (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* 1/2 (* (cos x) eps)) (neg eps)) (neg x) (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) (* (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (sin x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* 1/2 eps) x) (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* 1/2 (* (cos x) eps)) (neg eps)) (neg x) (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) (* (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
4.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (sin x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* 1/2 eps) x) (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* 1/2 (* (cos x) eps)) (neg eps)) (neg x) (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) (* (+ (* x (+ (* -1/4 x) (/ (+ (* -1/6 (* x x)) 1) eps))) 1/2) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))

simplify181.0ms (1.2%)

Memory

-3.4MiB live, 128.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	407	1600
1	1462	1524
2	5510	1516
0	8050	1406

Stop Event

1×	iter limit
1×	node limit

Counts

114 → 112

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)
(* -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)))))))
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))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* 2 x))
(* -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))))))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(* -1 x)
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (* x (+ (* -1/4 x) (/ 1 eps))))
(+ 1/2 (* x (+ (* x (- (* -1/6 (/ x eps)) 1/4)) (/ 1 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* 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 x)) (cos x))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))
(* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/6 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))
(* (pow x 3) (- (/ 1 (* eps (pow x 2))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))
(* (pow x 3) (- (+ (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 (pow x 3)))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 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 (- (* -1/2 (/ eps x)) 1)))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (/ 1 (* eps x)) 1/4) x)) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (/ 1/2 (pow x 2)) (/ 1 (* eps x))) 1/4) x)) (* 1/6 (/ 1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 eps)
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(pow eps 2)
(+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))
(* 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)))))))))
(/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)
(/ (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2))))) eps)
(* 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) (* 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))))))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* eps (+ 1/2 (/ x eps)))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

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

rewrite221.0ms (1.5%)

Memory

-27.6MiB live, 223.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	500
0	100	482
1	430	472
2	3621	472
0	8120	445

Stop Event

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

Counts

26 → 253

Calls

Call 1

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

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

eval55.0ms (0.4%)

Memory: 15.2MiB live, 67.5MiB allocated
Compiler: Compiled 16 024 to 1 961 computations (87.8% saved)

prune16.0ms (0.1%)

Memory

-22.5MiB live, 24.9MiB allocated

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	379	3	382
Fresh	1	2	3
Picked	2	3	5
Done	0	6	6
Total	382	14	396

Accuracy

100.0%

Counts

396 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	99.7%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.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))
✓	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) #s(approx (* (* 1/2 (* (cos x) eps)) (neg eps)) (.f64 (.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))))
✓	99.6%	#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)))
✓	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
✓	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
✓	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
✓	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) eps)) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	54.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) #s(approx (+ (* (* eps eps) (+ (* (* x x) 1/4) -1/2)) (* (neg x) eps)) (.f64 (.f64 (.f64 (.f64 eps x) eps) x) #s(literal 1/4 binary64)))))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 070 to 460 computations (57% saved)

regimes17.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

24 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
6.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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:

6.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.1%)

Memory

-29.3MiB live, 15.1MiB allocated

Counts

21 → 1

Calls

Call 1

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

Outputs
#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)))

Calls

3 calls:

11.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-24.2MiB live, 23.1MiB allocated

Counts

16 → 1

Calls

Call 1

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

6.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

-35.3MiB live, 18.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 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
98.8%	1	`x`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

-35.0MiB live, 12.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.5%	1	`x`
78.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify50.0ms (0.3%)

Memory

27.0MiB live, 72.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	320
1	187	318
2	352	316
3	639	316
4	1457	316
5	7678	316

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness1.1s (7.4%)

Memory

-15.0MiB live, 417.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	226	742
1	760	733
2	2444	711
3	5009	711
0	8441	659
0	407	1600
1	1462	1524
2	5510	1516
0	8050	1406
0	6	16
0	10	16
1	62	16
2	615	16
0	8130	16
0	29	128
0	47	128
1	175	128
2	1413	128
0	8759	128
0	268	916
1	922	880
2	3420	829
0	8311	771
0	105	296
1	308	293
2	779	293
3	2454	292
4	6244	292
0	8035	272

Stop Event

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

Compiler

Compiled 389 to 196 computations (49.6% saved)

preprocess90.0ms (0.6%)

Memory: -12.0MiB live, 39.4MiB allocated
Compiler: Compiled 688 to 248 computations (64% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze63.0ms (0.4%)

sample9.6s (63.5%)

explain269.0ms (1.8%)

preprocess50.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0%)

localize110.0ms (0.7%)

series20.0ms (0.1%)

simplify131.0ms (0.9%)

rewrite171.0ms (1.1%)

eval31.0ms (0.2%)

prune6.0ms (0%)

simplify147.0ms (1%)

localize365.0ms (2.4%)

series15.0ms (0.1%)

simplify225.0ms (1.5%)

rewrite213.0ms (1.4%)

eval49.0ms (0.3%)

prune11.0ms (0.1%)

simplify136.0ms (0.9%)

localize334.0ms (2.2%)

series26.0ms (0.2%)

simplify236.0ms (1.6%)

rewrite338.0ms (2.2%)

eval72.0ms (0.5%)

prune97.0ms (0.6%)

simplify199.0ms (1.3%)

localize329.0ms (2.2%)

series29.0ms (0.2%)

simplify181.0ms (1.2%)

rewrite221.0ms (1.5%)

eval55.0ms (0.4%)

prune16.0ms (0.1%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes21.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes14.0ms (0.1%)

regimes8.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify50.0ms (0.3%)

soundness1.1s (7.4%)

preprocess90.0ms (0.6%)

end0.0ms (0%)

Profiling