Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze45.0ms (0.3%)

Memory

37.0MiB live, 83.1MiB allocated; 9ms collecting garbage

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)

sample9.0s (61%)

Memory

-11.6MiB live, 7 222.3MiB allocated; 2.6s collecting garbage

Samples

4.0s	26 528×	0	invalid
2.8s	5 756×	2	valid
491.0ms	2 452×	1	valid
7.0ms	48×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.3s

ival-cos: 2.3s (43.5% of total)

const: 751.0ms (14.2% of total)

adjust: 446.0ms (8.5% of total)

ival-<=: 387.0ms (7.3% of total)

ival-<: 296.0ms (5.6% of total)

ival-mult: 261.0ms (4.9% of total)

ival-add: 229.0ms (4.3% of total)

ival-sub: 225.0ms (4.3% of total)

ival-fabs: 225.0ms (4.3% of total)

ival-and: 106.0ms (2% of total)

exact: 42.0ms (0.8% of total)

ival-assert: 12.0ms (0.2% of total)

Bogosity

explain285.0ms (1.9%)

Memory

-35.8MiB live, 296.8MiB allocated; 53ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
134	1	(-2.3839939815055273e-156 2.2132376463371385e-167)	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	1	(-94.74254507487623 6.216247652961803e-11)	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	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	135	0

Confusion

	Predicted +	Predicted -
+	134	0
-	1	121

Precision

0.9925925925925926

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	1	0	121

Precision?

0.9925925925925926

Recall?

1.0

Freqs

test

number	freq
0	121
1	135

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

206.0ms	362×	2	valid
20.0ms	148×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-cos: 159.0ms (80.1% of total)

adjust: 26.0ms (13.1% of total)

ival-sub: 9.0ms (4.5% of total)

ival-add: 4.0ms (2% of total)

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

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

preprocess14.0ms (0.1%)

Memory

35.1MiB live, 35.1MiB allocated; 0ms collecting garbage

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: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

-29.7MiB live, 15.9MiB allocated; 4ms collecting garbage

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)

localize137.0ms (0.9%)

Memory

2.6MiB live, 146.3MiB allocated; 13ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.020499716849389005	(cos.f64 (+.f64 x eps))
accuracy	30.24290750700567	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

120.0ms	181×	2	valid
10.0ms	74×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-cos: 70.0ms (59.8% of total)

adjust: 41.0ms (35% of total)

ival-sub: 3.0ms (2.6% of total)

ival-add: 2.0ms (1.7% of total)

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

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

series4.0ms (0%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

4 → 33

Calls

Call 1

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

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

Calls

6 calls:

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

simplify123.0ms (0.8%)

Memory

22.3MiB live, 157.0MiB allocated; 11ms collecting garbage

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)

rewrite200.0ms (1.4%)

Memory

-27.9MiB live, 164.6MiB allocated; 22ms collecting garbage

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)))

eval20.0ms (0.1%)

Memory: 23.4MiB live, 23.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 4 780 to 715 computations (85% saved)

prune8.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	152	9	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	10	162

Accuracy

99.8%

Counts

162 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	51.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	81.0%	(.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))
▶	51.8%	#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)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos 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))
▶	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 311 to 234 computations (24.8% saved)

simplify149.0ms (1%)

Memory

-6.2MiB live, 92.2MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	312
0	68	312
1	138	312
2	346	312
3	994	312
4	2612	312
5	4359	312
6	6959	312
0	8326	312

Stop Event

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

Calls

Call 1

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

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

localize417.0ms (2.8%)

Memory

-36.6MiB live, 349.4MiB allocated; 39ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.01953125	(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
accuracy	0.051462115408076686	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
accuracy	0.12890625	(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
accuracy	0.12890625	(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
accuracy	0.13803167954123896	#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	0.0	(sin.f64 x)
accuracy	0.0	(neg.f64 eps)
accuracy	0.00390625	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	12.767747981453958	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0.0	(cos.f64 eps)
accuracy	29.57922431754799	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	30.07264661464004	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.015625	(.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)
accuracy	0.1328125	(.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)
accuracy	0.19921875	(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))
accuracy	0.33984375	(*.f64 #s(literal 1/24 binary64) eps)

Samples

292.0ms	184×	2	valid
79.0ms	71×	1	valid
2.0ms	1×	3	valid

Compiler

Compiled 266 to 41 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 315.0ms

adjust: 103.0ms (32.6% of total)

ival-cos: 99.0ms (31.4% of total)

ival-mult: 54.0ms (17.1% of total)

ival-add: 38.0ms (12% of total)

ival-sub: 9.0ms (2.9% of total)

const: 7.0ms (2.2% of total)

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

ival-neg: 1.0ms (0.3% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

Counts

21 → 114

Calls

Call 1

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

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)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
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 (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))))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* -1 (* eps (sin x)))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* 1/6 (* eps (sin x)))
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (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 (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (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 (* -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)))
(* -1 eps)
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/24 eps)
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(cos 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)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (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)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* 1/24 eps) (* (* (sin x) eps) 1/6) (* (* (cos x) -1/2) eps))
5.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (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)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* 1/24 eps) (* (* (sin x) eps) 1/6) (* (* (cos x) -1/2) eps))
4.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (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)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* 1/24 eps) (* (* (sin x) eps) 1/6) (* (* (cos x) -1/2) eps))
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (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)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* 1/24 eps) (* (* (sin x) eps) 1/6) (* (* (cos x) -1/2) eps))
4.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (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)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* 1/24 eps) (* (* (sin x) eps) 1/6) (* (* (cos x) -1/2) eps))

simplify180.0ms (1.2%)

Memory

12.1MiB live, 55.3MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	385	1861
1	1437	1830
2	5744	1762
0	8331	1637

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)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
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 (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))))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* -1 (* eps (sin x)))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* 1/6 (* eps (sin x)))
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (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 (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (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 (* -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)))
(* -1 eps)
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/24 eps)
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(cos 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)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))

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)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) (.f64 eps (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) (.f64 eps eps) (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(fma.f64 (-.f64 (.f64 eps (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) eps))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(fma.f64 (.f64 eps (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) eps))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/36 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64))) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(* -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 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (.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))))) 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)) (-.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 (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 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) x) (neg.f64 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 #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 -1/4 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 #s(literal 1/24 binary64) (.f64 x x) #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 (fma.f64 (.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (.f64 x x) eps)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (-.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(* 1/6 (* eps x))
(.f64 (.f64 #s(literal 1/6 binary64) eps) x)
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) x)
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/36 binary64))) (.f64 (.f64 #s(literal 1/6 binary64) eps) x))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(.f64 (fma.f64 eps (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/30240 binary64) #s(literal 1/720 binary64))))) x)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (cos.f64 x))) eps) (sin.f64 x)) eps)
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (cos.f64 x))) eps) (sin.f64 x))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (cos.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(sin x)
(sin.f64 x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 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)
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (.f64 (sin.f64 x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))))
(* 1/6 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.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 (-.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 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 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 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (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 (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(neg.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(-.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 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #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 (-.f64 (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps))
1
#s(literal 1 binary64)
(+ 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) (*.f64 eps eps)) #s(literal 1/2 binary64)) 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 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 eps)
(neg.f64 eps)
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(neg.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.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))
(* 1/24 eps)
(*.f64 #s(literal 1/24 binary64) eps)
(* 1/24 (* (pow eps 4) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)) (cos.f64 x))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(cos eps)
(cos.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 (.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.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)
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps) eps)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(* -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 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps) eps)

rewrite219.0ms (1.5%)

Memory

5.8MiB live, 102.4MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	243
0	68	243
1	261	243
2	2129	243
0	8590	243

Stop Event

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

Counts

21 → 196

Calls

Call 1

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

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

eval40.0ms (0.3%)

Memory: 10.6MiB live, 55.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 11 298 to 1 375 computations (87.8% saved)

prune31.0ms (0.2%)

Memory

-10.3MiB live, 35.5MiB allocated; 3ms collecting garbage

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	301	17	318
Fresh	3	1	4
Picked	2	3	5
Done	0	1	1
Total	306	22	328

Accuracy

100.0%

Counts

328 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps)))
▶	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))))
	30.8%	#s(approx (- (cos (+ x eps)) (cos 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)))))))
▶	51.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #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)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))) eps))
	98.7%	#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 -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (neg.f64 eps)))
	98.2%	#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)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
▶	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) x) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	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 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	79.6%	#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)))
	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 318 to 854 computations (35.2% saved)

simplify142.0ms (1%)

Memory

17.3MiB live, 160.9MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(approx (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
cost-diff	4	(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
cost-diff	0	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)))
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff	4	(fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (* (cos x) eps) 1/2) (sin 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)))
cost-diff	0	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (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 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
cost-diff	2	(fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(sin.f64 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	74	673
0	114	669
1	237	668
2	629	658
3	1943	648
4	4037	638
5	5580	638
0	8053	601

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

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

localize546.0ms (3.7%)

Memory

5.7MiB live, 746.2MiB allocated; 142ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.078125	(.f64 (.f64 eps eps) x)
accuracy	0.1328125	(.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps)
accuracy	0.17578125	(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
accuracy	0.9729722486471329	#s(approx (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
accuracy	0.21875	(fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))
accuracy	0.3125	(.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
accuracy	0.6067574394271589	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
accuracy	0.12890625	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (neg.f64 eps))
accuracy	0.13803167954123896	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (neg.f64 eps)))
accuracy	1.0223650104276012	#s(approx (+ (* (* (cos x) eps) 1/2) (sin 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)))
accuracy	0.15299842215868076	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	29.57922431754799	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	30.07264661464004	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.01171875	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))
accuracy	0.01171875	(*.f64 (cos.f64 x) 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	0.13803167954123896	#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

361.0ms	183×	2	valid
90.0ms	71×	1	valid
6.0ms	2×	3	valid

Compiler

Compiled 411 to 69 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 385.0ms

ival-cos: 115.0ms (29.8% of total)

adjust: 102.0ms (26.5% of total)

ival-mult: 88.0ms (22.8% of total)

ival-add: 46.0ms (11.9% of total)

ival-sub: 15.0ms (3.9% of total)

const: 13.0ms (3.4% of total)

ival-sin: 4.0ms (1% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

series44.0ms (0.3%)

Memory

-10.8MiB live, 33.1MiB allocated; 19ms collecting garbage

Counts

26 → 154

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

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))))
(* 1/2 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))))))
(- (* 1/6 (pow eps 2)) 1)
(- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
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 (- (* 1/6 (pow eps 2)) 1)))
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* (pow eps 2) 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)
(* -1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/4 eps) (+ (* 1/2 (/ eps (pow x 2))) (/ 1 x))))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* 1/6 (* (pow eps 2) x))
(* x (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (cos x))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/6 (pow eps 2)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* eps (sin 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)))
(* (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 (* -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)))
(+ x (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(- (* 1/6 (pow x 2)) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* eps (- (* 1/6 (* eps x)) 1/2))
(* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (pow eps 2))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(cos eps)
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/24 (pow eps 3))
(* (pow eps 3) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 3) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1 (* (pow eps 3) (- (* -1/6 (/ x eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/6 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	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)) (- (cos eps) 1) (cos eps) (+ (* (+ (* -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)) (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (cos x) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x))
8.0ms	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)) (- (cos eps) 1) (cos eps) (+ (* (+ (* -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)) (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (cos x) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x))
5.0ms	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)) (- (cos eps) 1) (cos eps) (+ (* (+ (* -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)) (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (cos x) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x))
5.0ms	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)) (- (cos eps) 1) (cos eps) (+ (* (+ (* -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)) (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (cos x) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x))
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)) (- (cos eps) 1) (cos eps) (+ (* (+ (* -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)) (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (cos x) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x))

simplify215.0ms (1.5%)

Memory

2.7MiB live, 115.9MiB allocated; 122ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	499	2457
1	1791	2425
2	6831	2409
0	8151	2234

Stop Event

1×	iter limit
1×	node limit

Counts

154 → 152

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))))
(* 1/2 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))))))
(- (* 1/6 (pow eps 2)) 1)
(- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
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 (- (* 1/6 (pow eps 2)) 1)))
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* (pow eps 2) 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)
(* -1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/4 eps) (+ (* 1/2 (/ eps (pow x 2))) (/ 1 x))))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* 1/6 (* (pow eps 2) x))
(* x (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (cos x))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/6 (pow eps 2)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* eps (sin 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)))
(* (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 (* -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)))
(+ x (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(- (* 1/6 (pow x 2)) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* eps (- (* 1/6 (* eps x)) 1/2))
(* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (pow eps 2))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(cos eps)
(* eps (+ 1/2 (* -1/4 (pow x 2))))
(* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/24 (pow eps 3))
(* (pow eps 3) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 3) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1 (* (pow eps 3) (- (* -1/6 (/ x eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/6 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))

Outputs
(* -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 eps) x (.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)))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (.f64 (.f64 (*.f64 eps x) eps) x) #s(literal 1/4 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 (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 (.f64 eps x) eps) x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) 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 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 (.f64 (.f64 eps x) eps) x) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) x) x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (*.f64 x x)))
(- (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 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (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)))
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)))))
(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))
(- (* 1/6 (pow eps 2)) 1)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)
(fma.f64 #s(literal 1/4 binary64) (.f64 eps x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) eps (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) x))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) x) #s(literal -1/2 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.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 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64))
(* 1/4 eps)
(*.f64 #s(literal 1/4 binary64) eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps x)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(* (pow eps 2) x)
(.f64 (.f64 eps x) eps)
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(* -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)
(* -1/4 (* eps (pow x 2)))
(.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps)
(* (pow x 2) (+ (* -1/4 eps) (/ 1 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) x)
(* (pow x 2) (+ (* -1/4 eps) (+ (* 1/2 (/ eps (pow x 2))) (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x) x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(+ (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 2) (- (* 1/6 (pow eps 2)) 1)))
(.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) x) #s(literal -1/6 binary64))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
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(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
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(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps)
(* -1 (* (pow eps 3) (- (* -1/6 (/ x eps)) 1/24)))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (.f64 (/.f64 x eps) #s(literal -1/6 binary64)) #s(literal 1/24 binary64)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/6 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (neg.f64 eps)) #s(literal 1/24 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) eps))) eps) eps)

rewrite180.0ms (1.2%)

Memory

-10.7MiB live, 127.5MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	557
0	114	553
1	469	552
2	3710	552
0	8544	533

Stop Event

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

Counts

26 → 232

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

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

eval66.0ms (0.5%)

Memory: -2.7MiB live, 57.5MiB allocated; 3ms collecting garbage
Compiler: Compiled 20 633 to 2 283 computations (88.9% saved)

prune19.0ms (0.1%)

Memory

28.9MiB live, 28.9MiB allocated; 0ms collecting garbage

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	389	8	397
Fresh	4	9	13
Picked	4	1	5
Done	0	4	4
Total	397	22	419

Accuracy

100.0%

Counts

419 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps)))
▶	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))) (neg.f64 eps))))
✓	51.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #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)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) #s(approx (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.7%	#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 -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	98.2%	#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)))
	36.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x) #s(literal 2 binary64))))) (neg.f64 eps)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
▶	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps)))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps #s(approx (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	79.6%	#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)))
▶	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 458 to 919 computations (37% saved)

simplify108.0ms (0.7%)

Memory

-2.3MiB live, 45.2MiB allocated; 1ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	675
0	116	669
1	249	664
2	710	646
3	2160	643
4	4753	642
5	7792	642
0	8043	628

Stop Event

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

Calls

Call 1

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

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

localize424.0ms (2.9%)

Memory

-11.8MiB live, 218.2MiB allocated; 20ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))) (neg.f64 eps)))
accuracy	0.07421875	(.f64 (.f64 x x) eps)
accuracy	0.13803167954123896	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))) (neg.f64 eps))))
accuracy	0.6632264004209038	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
accuracy	0.21875	(fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))
accuracy	0.3125	(.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
accuracy	0.6055579093234951	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x)
accuracy	0.12890625	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps))
accuracy	0.13803167954123896	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps)))
accuracy	1.0223650104276012	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x)))
accuracy	0.0	(*.f64 (neg.f64 x) eps)
accuracy	0.0	(neg.f64 x)
accuracy	1.008267634078385	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	12.767747981453958	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0.00390625	(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps)
accuracy	0.01171875	(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.051462115408076686	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps)))
accuracy	0.1171875	(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps))

Samples

264.0ms	179×	2	valid
65.0ms	74×	1	valid
5.0ms	2×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 415 to 69 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 281.0ms

ival-mult: 89.0ms (31.7% of total)

adjust: 82.0ms (29.2% of total)

ival-cos: 56.0ms (19.9% of total)

ival-add: 31.0ms (11% of total)

const: 10.0ms (3.6% of total)

ival-sub: 6.0ms (2.1% of total)

ival-sin: 4.0ms (1.4% of total)

ival-neg: 2.0ms (0.7% of total)

exact: 1.0ms (0.4% of total)

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

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

series36.0ms (0.2%)

Memory

-6.7MiB live, 36.1MiB allocated; 8ms collecting garbage

Counts

28 → 137

Calls

Call 1

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

Outputs
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(- (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 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 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)))))))))
(* -1 x)
(+ (* -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 (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (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))))))))
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))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))))))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))) (* 1/120 (* eps (- (* 1/6 (pow eps 2)) 1)))))))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
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))))))
(* eps (pow x 2))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* eps (cos x)))
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* -1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/4 eps) (+ (* 1/2 (/ eps (pow x 2))) (/ 1 x))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(sin x)
(* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* eps (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* 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)))
(+ x (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (pow eps 2))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (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 eps))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* 1/6 (pow eps 3))
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(- (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 eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (/ (sin x) (pow eps 2)))))
(* -1 (* eps (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (* (- (* (* eps eps) 1/6) 1) eps) (- (cos (+ x eps)) (cos x)) (+ (* (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) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps) (+ (* (+ (* -1/4 (* x x)) 1/2) eps) x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (cos x) eps) (* (* x x) eps))
5.0ms	eps	@	-inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (* (- (* (* eps eps) 1/6) 1) eps) (- (cos (+ x eps)) (cos x)) (+ (* (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) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps) (+ (* (+ (* -1/4 (* x x)) 1/2) eps) x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (cos x) eps) (* (* x x) eps))
5.0ms	x	@	inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (* (- (* (* eps eps) 1/6) 1) eps) (- (cos (+ x eps)) (cos x)) (+ (* (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) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps) (+ (* (+ (* -1/4 (* x x)) 1/2) eps) x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (cos x) eps) (* (* x x) eps))
5.0ms	eps	@	0	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (* (- (* (* eps eps) 1/6) 1) eps) (- (cos (+ x eps)) (cos x)) (+ (* (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) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps) (+ (* (+ (* -1/4 (* x x)) 1/2) eps) x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (cos x) eps) (* (* x x) eps))
4.0ms	x	@	-inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (* (- (* (* eps eps) 1/6) 1) eps) (- (cos (+ x eps)) (cos x)) (+ (* (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) (* (* (+ (* (* eps eps) 1/6) -1) (sin x)) eps) (+ (* (+ (* -1/4 (* x x)) 1/2) eps) x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) (* (* eps eps) 1/6) (* (cos x) eps) (* (* x x) eps))

simplify151.0ms (1%)

Memory

18.2MiB live, 121.7MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	499	2240
1	1816	2187
2	7212	2183
0	8249	2036

Stop Event

1×	iter limit
1×	node limit

Counts

137 → 135

Calls

Call 1

Inputs
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(- (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 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 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)))))))))
(* -1 x)
(+ (* -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 (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (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))))))))
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))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))))))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))) (* 1/120 (* eps (- (* 1/6 (pow eps 2)) 1)))))))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
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))))))
(* eps (pow x 2))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* eps (cos x)))
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* -1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1/4 eps) (+ (* 1/2 (/ eps (pow x 2))) (/ 1 x))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(sin x)
(* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* eps (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* (pow x 2) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* 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)))
(+ x (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (pow eps 2))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (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 eps))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* 1/6 (pow eps 3))
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(- (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 eps)) (* 1/4 (pow x 2))) 1/2)))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (/ (sin x) (pow eps 2)))))
(* -1 (* eps (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))

Outputs
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (*.f64 eps eps) #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)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/4 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/48 binary64) eps)) x) x (.f64 #s(literal 1/4 binary64) eps)) (.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(-.f64 (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1440 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) 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)) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/6 binary64) eps)) (.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)))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) x) x (.f64 #s(literal 1/6 binary64) eps)) (.f64 (neg.f64 x) eps))
(* -1 x)
(neg.f64 x)
(+ (* -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 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) x (neg.f64 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 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 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 (*.f64 x x) #s(literal -1/4 binary64) #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 -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(* eps (- (* 1/6 (pow eps 2)) 1))
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(fma.f64 (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(fma.f64 (.f64 (.f64 (.f64 x x) eps) eps) #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #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 (fma.f64 (.f64 (.f64 (.f64 x x) eps) eps) #s(literal -1/48 binary64) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) 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 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) eps) eps) #s(literal 1/1440 binary64) (.f64 (.f64 #s(literal -1/48 binary64) eps) eps)) x) x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (.f64 x 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)
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))) (* eps (- (* 1/6 (pow eps 2)) 1))))
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(.f64 (.f64 #s(literal -1/36 binary64) (*.f64 eps x)) eps)
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) x)) eps) eps)
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps)) eps) eps)
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 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 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))
(* -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 eps)) (* 1/4 (pow x 2))) 1/2)))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (-.f64 (/.f64 x (neg.f64 eps)) #s(literal 1/2 binary64))) (neg.f64 eps))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(.f64 (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) x) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x (/.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))) #s(literal 1/2 binary64)) (neg.f64 eps))))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 x eps) #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) x) x (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) eps) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (/ (sin x) (pow eps 2)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (/.f64 (sin.f64 x) eps) eps)))
(* -1 (* eps (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps)))))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) (/.f64 x eps)) (neg.f64 eps))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) eps))) eps) eps)

rewrite166.0ms (1.1%)

Memory

17.9MiB live, 106.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	552
0	116	546
1	452	541
2	3604	541
0	8207	520

Stop Event

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

Counts

28 → 270

Calls

Call 1

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

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

eval122.0ms (0.8%)

Memory: -47.2MiB live, 57.2MiB allocated; 32ms collecting garbage
Compiler: Compiled 22 765 to 2 218 computations (90.3% saved)

prune27.0ms (0.2%)

Memory

35.6MiB live, 35.6MiB allocated; 0ms collecting garbage

Pruning

23 alts after pruning (15 fresh and 8 done)

	Pruned	Kept	Total
New	412	6	418
Fresh	3	9	12
Picked	2	3	5
Done	0	5	5
Total	417	23	440

Accuracy

100.0%

Counts

440 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) eps)))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64)) eps)))
✓	51.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #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)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) #s(approx (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.7%	#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)))
	98.2%	#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)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
✓	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps)))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps #s(approx (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* (cos x) eps)) (neg eps))) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps #s(approx ( -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (.f64 #s(literal 1/6 binary64) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	27.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64))) x (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)))) x) #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64))) x (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)))) x (.f64 #s(literal 1/2 binary64) (.f64 eps eps))))))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
	79.6%	#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)))
✓	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 2 417 to 891 computations (63.1% saved)

regimes29.0ms (0.2%)

Memory

-25.0MiB live, 21.7MiB allocated; 1ms collecting garbage

Counts

41 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (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 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 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)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) x) (neg.f64 eps)) x (.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 (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))) (neg.f64 eps)))
#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 (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps #s(approx (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps #s(approx ( -1/6 (* (- (* (* eps eps) 1/6) 1) x)) (.f64 #s(literal 1/6 binary64) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) #s(literal -1/2 binary64))) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 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 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) #s(approx (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) 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) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 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) (.f64 (.f64 #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
(-.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 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
#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 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) 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))
#s(approx (- (cos (+ x eps)) (cos 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))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64))) x (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)))) x) #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64))) x (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)))) x (.f64 #s(literal 1/2 binary64) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (.f64 eps x) #s(literal -1/4 binary64) #s(literal 1 binary64)) x) #s(literal 2 binary64))))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos 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)))))))

Outputs

#s(approx (- (cos (+ x eps)) (cos 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))

Calls

3 calls:

10.0ms	eps
9.0ms	x
7.0ms	(-.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)

regimes25.0ms (0.2%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms collecting garbage

Counts

37 → 1

Calls

Call 1

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

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

regimes23.0ms (0.2%)

Memory

-28.7MiB live, 18.2MiB allocated; 1ms collecting garbage

Counts

32 → 1

Calls

Call 1

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

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:

8.0ms	x
7.0ms	eps
6.0ms	(-.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)

regimes21.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated; 0ms collecting garbage

Counts

30 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated; 0ms collecting garbage

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

6.0ms	x
6.0ms	eps
5.0ms	(-.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)

regimes19.0ms (0.1%)

Memory

-36.5MiB live, 14.0MiB allocated; 4ms collecting garbage

Counts

23 → 1

Calls

Call 1

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

Calls

3 calls:

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

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)

regimes12.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes11.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated; 0ms collecting garbage

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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:

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

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.8%	1	`eps`
98.8%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (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 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 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)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x))) x) (- (* (* eps eps) 1/6) 1)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin 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))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) x) (neg.f64 eps)) x (.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 (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))) (neg.f64 eps)))
#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 -1/4 binary64) 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	eps
3.0ms	x
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

-39.0MiB live, 8.2MiB allocated; 1ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (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 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 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)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (* eps (+ (* 1/4 eps) (* -1/6 (* (- (* (* eps eps) 1/6) 1) x)))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps x))) (neg.f64 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 eps) x (.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
98.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.4%	1	`eps`
98.4%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (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
98.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.2%	1	`x`
98.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs

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

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (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:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
51.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
51.8%	1	`eps`
51.8%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify67.0ms (0.5%)

Memory

-20.4MiB live, 26.2MiB allocated; 1ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	156	577
1	296	577
2	694	575
3	1916	567
4	3893	565
5	5038	565
6	7286	565

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations1.2s (8.1%)

Memory

13.4MiB live, 430.7MiB allocated; 44ms collecting garbage

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
0	385	1861
1	1437	1830
2	5744	1762
0	8331	1637
0	499	2240
1	1816	2187
2	7212	2183
0	8249	2036
0	75	552
0	116	546
1	452	541
2	3604	541
0	8207	520
0	40	243
0	68	243
1	261	243
2	2129	243
0	8590	243
0	499	2457
1	1791	2425
2	6831	2409
0	8151	2234

Stop Event

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

Compiler

Compiled 577 to 159 computations (72.4% saved)

preprocess120.0ms (0.8%)

Memory: 17.9MiB live, 72.6MiB allocated; 14ms collecting garbage
Compiler: Compiled 1 202 to 360 computations (70% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze45.0ms (0.3%)

sample9.0s (61%)

explain285.0ms (1.9%)

preprocess14.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize137.0ms (0.9%)

series4.0ms (0%)

simplify123.0ms (0.8%)

rewrite200.0ms (1.4%)

eval20.0ms (0.1%)

prune8.0ms (0.1%)

simplify149.0ms (1%)

localize417.0ms (2.8%)

series29.0ms (0.2%)

simplify180.0ms (1.2%)

rewrite219.0ms (1.5%)

eval40.0ms (0.3%)

prune31.0ms (0.2%)

simplify142.0ms (1%)

localize546.0ms (3.7%)

series44.0ms (0.3%)

simplify215.0ms (1.5%)

rewrite180.0ms (1.2%)

eval66.0ms (0.5%)

prune19.0ms (0.1%)

simplify108.0ms (0.7%)

localize424.0ms (2.9%)

series36.0ms (0.2%)

simplify151.0ms (1%)

rewrite166.0ms (1.1%)

eval122.0ms (0.8%)

prune27.0ms (0.2%)

regimes29.0ms (0.2%)

regimes25.0ms (0.2%)

regimes23.0ms (0.2%)

regimes21.0ms (0.1%)

regimes18.0ms (0.1%)

regimes19.0ms (0.1%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify67.0ms (0.5%)

derivations1.2s (8.1%)

preprocess120.0ms (0.8%)

end0.0ms (0%)

Profiling