Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

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

analyze538.0ms (3.7%)

Memory

-216.5MiB live, 41.3MiB allocated; 882ms 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)

sample8.4s (57.4%)

Memory

117.0MiB live, 6 793.4MiB allocated; 1.3s collecting garbage

Samples

3.3s	26 528×	0	invalid
2.8s	5 756×	2	valid
584.0ms	2 452×	1	valid
6.0ms	48×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.4s

ival-cos: 2.2s (40.6% of total)

const: 740.0ms (13.7% of total)

adjust: 569.0ms (10.6% of total)

ival-<=: 409.0ms (7.6% of total)

ival-mult: 309.0ms (5.7% of total)

ival-fabs: 272.0ms (5% of total)

ival-sub: 269.0ms (5% of total)

ival-add: 264.0ms (4.9% of total)

ival-<: 195.0ms (3.6% of total)

ival-and: 112.0ms (2.1% of total)

exact: 47.0ms (0.9% of total)

ival-assert: 14.0ms (0.3% of total)

Bogosity

explain235.0ms (1.6%)

Memory

-32.3MiB live, 205.6MiB allocated; 20ms 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

150.0ms	362×	2	valid
24.0ms	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: 148.0ms

ival-cos: 102.0ms (68.8% of total)

adjust: 30.0ms (20.2% of total)

ival-sub: 11.0ms (7.4% of total)

ival-add: 4.0ms (2.7% of total)

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

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

preprocess250.0ms (1.7%)

Memory

28.0MiB live, 171.2MiB allocated; 17ms 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	117	41
4	125	41
5	147	41
6	231	41
7	792	41
8	5144	41
0	6	7
0	10	7
1	22	7
2	40	7
3	65	7
4	78	7
5	100	7
6	184	7
7	742	7
8	5073	7
0	8505	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

simplify144.0ms (1%)

Memory

14.1MiB live, 103.5MiB allocated; 8ms 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	65	18
4	78	18
5	100	18
6	184	18
7	742	18
8	5073	18
0	8505	18

Stop Event

1×	iter limit
1×	node limit
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)

localize154.0ms (1.1%)

Memory

-11.9MiB live, 140.2MiB allocated; 12ms 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

95.0ms	181×	2	valid
52.0ms	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: 135.0ms

ival-cos: 115.0ms (85.4% of total)

adjust: 13.0ms (9.7% of total)

ival-sub: 3.0ms (2.2% of total)

ival-add: 2.0ms (1.5% of total)

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

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

series4.0ms (0%)

Memory

5.5MiB live, 5.5MiB 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))

simplify141.0ms (1%)

Memory

9.1MiB live, 152.2MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	308	293
2	814	293
3	2685	292
4	6556	292
0	8099	272

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite154.0ms (1.1%)

Memory

-5.1MiB live, 86.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	62	16
2	615	16
0	8141	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)))))
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(fma.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 eps 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 (neg.f64 (cos.f64 x)) (cos.f64 x)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
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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))
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(/.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))
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(-.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)))
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(+.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)))
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(/.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)))

eval33.0ms (0.2%)

Memory: -28.3MiB live, 17.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 4 780 to 712 computations (85.1% saved)

prune8.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	11	162

Accuracy

99.8%

Counts

162 → 11

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))
	53.5%	(.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)))))
▶	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)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #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)))

Compiler

Compiled 387 to 266 computations (31.3% saved)

simplify168.0ms (1.2%)

Memory

1.1MiB live, 51.2MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
cost-diff	1	(+.f64 (+.f64 eps x) x)
cost-diff	1	(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
cost-diff	4	(-.f64 (+.f64 eps x) x)
cost-diff	0	(*.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 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
cost-diff	1	(fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	320
0	70	316
1	129	308
2	269	300
3	681	292
4	2341	292
0	8314	286

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

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

localize380.0ms (2.6%)

Memory

12.8MiB live, 202.2MiB allocated; 12ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.050533741949228786	(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
accuracy	0.12890625	(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
accuracy	0.31640625	(+.f64 (+.f64 eps x) x)
accuracy	25.10622895191232	(-.f64 (+.f64 eps x) x)
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 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
accuracy	0.1328125	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.328125	(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
accuracy	0.34375	(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))

Samples

285.0ms	184×	2	valid
46.0ms	71×	1	valid
2.0ms	1×	3	valid

Compiler

Compiled 286 to 42 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-cos: 85.0ms (35.9% of total)

adjust: 53.0ms (22.4% of total)

ival-mult: 47.0ms (19.8% of total)

ival-add: 14.0ms (5.9% of total)

ival-sub: 11.0ms (4.6% of total)

const: 10.0ms (4.2% of total)

ival-sin: 9.0ms (3.8% of total)

ival-div: 5.0ms (2.1% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series41.0ms (0.3%)

Memory

2.1MiB live, 47.3MiB allocated; 6ms collecting garbage

Counts

24 → 145

Calls

Call 1

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

Outputs
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (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 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (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 (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
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))))))
(+ eps (* 2 x))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -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))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/24 (* eps (cos x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1/2 (cos x))
(+ (* -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)))
(* 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))
(* (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)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/6 (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) 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)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos 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 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	-inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (- (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) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* (cos x) eps) 1/24) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
6.0ms	x	@	inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (- (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) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* (cos x) eps) 1/24) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
5.0ms	eps	@	-inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (- (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) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* (cos x) eps) 1/24) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
5.0ms	x	@	0	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (- (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) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* (cos x) eps) 1/24) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))
4.0ms	eps	@	0	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (- (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) (- (+ eps x) x) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (* (cos x) eps) 1/24) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)))

simplify165.0ms (1.1%)

Memory

-10.5MiB live, 209.3MiB allocated; 39ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	493	2235
1	1863	2188
2	7542	2178
0	8259	1998

Stop Event

1×	iter limit
1×	node limit

Counts

145 → 143

Calls

Call 1

Inputs
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (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 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (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 (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
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))))))
(+ eps (* 2 x))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -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))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/24 (* eps (cos x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1/2 (cos x))
(+ (* -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)))
(* 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))
(* (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)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/6 (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) 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)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos 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 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))

Outputs
(- (* 1/24 (pow eps 2)) 1/2)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 #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)))
(* (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 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (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 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) x) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (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 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))
(* 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)
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (+ (* eps (+ 1/4 (* -1/48 (pow eps 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #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 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) 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))
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 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(+ (* -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 #s(literal -1/2 binary64) (*.f64 eps eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 (-.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 #s(literal -1/2 binary64) (.f64 eps eps)))
(* 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 (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)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x x)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 x x)))
(* 1/24 eps)
(*.f64 #s(literal 1/24 binary64) eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/48 binary64) (*.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
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(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps)
(* (pow eps 2) (+ (* -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)) (*.f64 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 (pow.f64 eps #s(literal 4 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 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 (sin.f64 x) #s(literal -1/6 binary64) (/.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 (sin.f64 x) #s(literal 1/6 binary64))) (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 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite106.0ms (0.7%)

Memory

-3.5MiB live, 135.2MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	268
0	70	256
1	259	252
0	2220	248

Stop Event

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

Counts

24 → 227

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 3 binary64)) (pow.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (neg.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps) #s(literal -1/2 binary64)) (cos.f64 x)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64)))
(fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)))))
(-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (neg.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (neg.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))))) eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (neg.f64 eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) #s(literal 2 binary64)))))
(+.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64)))
(+.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) 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 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
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(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps) eps))
(fma.f64 eps (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) eps)))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) eps) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps) eps))
(+.f64 (.f64 eps (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps (.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))) eps)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(fma.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))

eval50.0ms (0.3%)

Memory: -26.0MiB live, 68.5MiB allocated; 5ms collecting garbage
Compiler: Compiled 13 267 to 1 948 computations (85.3% saved)

prune20.0ms (0.1%)

Memory

37.2MiB live, 37.2MiB allocated; 0ms collecting garbage

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	364	18	382
Fresh	3	2	5
Picked	3	2	5
Done	0	1	1
Total	370	23	393

Accuracy

100.0%

Counts

393 → 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))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (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)))
	99.2%	#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)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (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)))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
▶	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 339 to 896 computations (33.1% saved)

simplify165.0ms (1.1%)

Memory

0.5MiB live, 142.3MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
cost-diff	2	(fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
cost-diff	0	#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
cost-diff	0	(-.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps)
cost-diff	0	(.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
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	(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx ( (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
cost-diff	0	(-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx ( (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	832
0	116	832
1	211	826
2	526	826
3	1726	818
4	4854	818
0	8523	796

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

localize491.0ms (3.4%)

Memory

-13.1MiB live, 448.5MiB allocated; 74ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps)
accuracy	0.1328125	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps)
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
accuracy	0.9881040150857142	#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
accuracy	0.3125	(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
accuracy	0.33984375	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.6067574394271589	#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
accuracy	0.07421875	(.f64 (.f64 x x) eps)
accuracy	0.12890625	(.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))
accuracy	0.605557897718781	#s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))
accuracy	12.767747981453958	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
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	0.1328125	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.328125	(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps)))
accuracy	0.33984375	(*.f64 #s(literal 1/24 binary64) eps)
accuracy	0.9694068852026226	#s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps))

Samples

360.0ms	182×	2	valid
64.0ms	71×	1	valid
9.0ms	3×	3	valid

Compiler

Compiled 538 to 58 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 362.0ms

adjust: 115.0ms (31.8% of total)

ival-cos: 98.0ms (27.1% of total)

ival-mult: 72.0ms (19.9% of total)

ival-add: 39.0ms (10.8% of total)

const: 16.0ms (4.4% of total)

ival-sub: 16.0ms (4.4% of total)

ival-sin: 4.0ms (1.1% 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)

series31.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Counts

29 → 139

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx ( (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx ( (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))
(.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)
(-.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x))
#s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps))
(*.f64 #s(literal 1/24 binary64) eps)
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps)))
(.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))
(.f64 (.f64 x x) eps)
(*.f64 #s(literal 1/6 binary64) eps)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #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 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (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 (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 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 (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 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 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(* 1/6 (* eps (pow x 2)))
(* eps (pow x 2))
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (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)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* 1/6 (* eps x))
(* x (- (+ (* 1/24 (/ (pow eps 2) x)) (* 1/6 eps)) (* 1/2 (/ 1 x))))
(* 1/24 (* eps (cos x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/24 (pow eps 2)) 1/2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) 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))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
1
(+ 1 (* -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)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* 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 (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)
(* 1/6 (sin x))
(* 1/6 eps)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* 1/24 (pow eps 2))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (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)
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* (pow eps 2) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 2) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(- (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 (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* (pow eps 2) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (* (cos x) eps) 1/24) (* 1/24 eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* (* eps eps) 1/24) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps))
5.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (* (cos x) eps) 1/24) (* 1/24 eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* (* eps eps) 1/24) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps))
5.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (* (cos x) eps) 1/24) (* 1/24 eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* (* eps eps) 1/24) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps))
4.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (* (cos x) eps) 1/24) (* 1/24 eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* (* eps eps) 1/24) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps))
4.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (- (* (* (* x x) eps) 1/6) eps) x) (- (* (* (* x x) eps) 1/6) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (* (cos x) eps) 1/24) (* 1/24 eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (* x x) eps) 1/6) (* (* x x) eps) (* 1/6 eps) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* (* eps eps) 1/24) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps))

simplify147.0ms (1%)

Memory

3.2MiB live, 51.8MiB allocated; 38ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	514	2414
1	1868	2354
0	8059	2132

Stop Event

1×	iter limit
1×	node limit

Counts

139 → 139

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 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (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 (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 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 (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 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 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(* 1/6 (* eps (pow x 2)))
(* eps (pow x 2))
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (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)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* 1/6 (* eps x))
(* x (- (+ (* 1/24 (/ (pow eps 2) x)) (* 1/6 eps)) (* 1/2 (/ 1 x))))
(* 1/24 (* eps (cos x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/24 (pow eps 2)) 1/2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) 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))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
1
(+ 1 (* -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)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* 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 (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)
(* 1/6 (sin x))
(* 1/6 eps)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* 1/24 (pow eps 2))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (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)
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* (pow eps 2) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 2) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(- (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 (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* (pow eps 2) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))

Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (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)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.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 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) x) eps (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) 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 (fma.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)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (fma.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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (fma.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 (+ (* eps (+ 1/4 (* -1/48 (pow eps 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (.f64 (fma.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 eps eps) x) #s(literal 1/6 binary64) (.f64 (fma.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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (fma.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 (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) eps #s(literal 1/4 binary64)) eps (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64))) x)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(* -1 (* eps x))
(*.f64 (neg.f64 eps) x)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 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)) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/6 binary64) eps)) (.f64 (neg.f64 eps) x))
(* 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 eps) x))
(* -1 eps)
(neg.f64 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(-.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps)
(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64))
(* 1/24 eps)
(*.f64 #s(literal 1/24 binary64) eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) eps)
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/17280 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/576 binary64) eps)) x) x (.f64 #s(literal -1/48 binary64) eps)) (.f64 x x) (*.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(* 1/6 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))
(* eps (pow x 2))
(.f64 (.f64 x x) eps)
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) eps #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* 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 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(- (* 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 #s(literal 1/6 binary64) (sin.f64 x))) eps (.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))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* 1/6 (* eps (pow x 3)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64)) eps)
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (neg.f64 (fma.f64 #s(literal -1/6 binary64) eps (/.f64 eps (.f64 x x)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)))
(* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))
(.f64 (+.f64 (/.f64 (-.f64 (fma.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) (/.f64 #s(literal 1 binary64) x)) x) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(.f64 (-.f64 (+.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x)) (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* 1/6 (* eps x))
(.f64 (.f64 #s(literal 1/6 binary64) eps) x)
(* x (- (+ (* 1/24 (/ (pow eps 2) x)) (* 1/6 eps)) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) x)
(* 1/24 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) x)
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
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(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(.f64 (neg.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) x) x (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64)) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(.f64 (neg.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) x) x (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x (/.f64 (fma.f64 (neg.f64 x) (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) eps) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (neg.f64 eps) (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) (+ 1/48 (* 1/36 (/ x eps)))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (/.f64 x eps) #s(literal 1/48 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/48 binary64) (/.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)) (neg.f64 eps))) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -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))) eps)) (*.f64 eps eps))

rewrite162.0ms (1.1%)

Memory

-29.7MiB live, 64.6MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	682
0	116	682
1	447	676
2	3655	676
0	8176	650

Stop Event

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

Counts

29 → 191

Calls

Call 1

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

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

eval43.0ms (0.3%)

Memory: 36.3MiB live, 36.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 19 780 to 2 036 computations (89.7% saved)

prune23.0ms (0.2%)

Memory

-21.5MiB live, 25.1MiB allocated; 1ms collecting garbage

Pruning

26 alts after pruning (20 fresh and 6 done)

	Pruned	Kept	Total
New	322	7	329
Fresh	2	13	15
Picked	2	3	5
Done	0	3	3
Total	326	26	352

Accuracy

100.0%

Counts

352 → 26

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))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (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)))
	99.2%	#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)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x))) 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)))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
✓	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
▶	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 835 to 1 199 computations (34.7% saved)

simplify128.0ms (0.9%)

Memory

-13.0MiB live, 40.2MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps)
cost-diff	0	(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
cost-diff	0	#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
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	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	(sin.f64 x)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (neg.f64 eps))))
cost-diff	1	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (neg.f64 eps))
cost-diff	2	(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (neg.f64 eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	825
0	120	821
1	236	808
2	598	806
3	1703	798
4	4353	798
0	8084	747

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

localize483.0ms (3.3%)

Memory

37.3MiB live, 350.9MiB allocated; 70ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.13280342895323055	#s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))
accuracy	0.1328125	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps)
accuracy	0.30859375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.9881040150857142	#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64))))
accuracy	0.30859375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.33984375	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.6067574394271589	#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
accuracy	25.579080561131796	#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (*.f64 #s(literal 1/6 binary64) x))
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	0.0	(*.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	0.01171875	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (neg.f64 eps))
accuracy	0.01171875	(*.f64 eps (cos.f64 x))
accuracy	0.015625	(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (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 eps (cos.f64 x))) (neg.f64 eps))))

Samples

318.0ms	179×	2	valid
79.0ms	74×	1	valid
5.0ms	2×	3	valid
1.0ms	1×	0	valid

Compiler

Compiled 447 to 69 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 337.0ms

adjust: 118.0ms (35% of total)

ival-mult: 91.0ms (27% of total)

ival-cos: 57.0ms (16.9% of total)

ival-add: 30.0ms (8.9% of total)

const: 24.0ms (7.1% of total)

ival-sub: 10.0ms (3% of total)

ival-sin: 4.0ms (1.2% of total)

ival-neg: 2.0ms (0.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series23.0ms (0.2%)

Memory

21.6MiB live, 21.6MiB allocated; 0ms collecting garbage

Counts

26 → 146

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (* (* 1/2 (* eps (cos x))) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* eps (cos x)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* 1/6 eps) (* 1/6 x) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)))
4.0ms	x	@	-inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (* (* 1/2 (* eps (cos x))) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* eps (cos x)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* 1/6 eps) (* 1/6 x) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)))
3.0ms	eps	@	inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (* (* 1/2 (* eps (cos x))) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* eps (cos x)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* 1/6 eps) (* 1/6 x) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)))
3.0ms	eps	@	0	((+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (* (* 1/2 (* eps (cos x))) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* eps (cos x)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* 1/6 eps) (* 1/6 x) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)))
3.0ms	eps	@	-inf	((+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (* (* 1/2 (* eps (cos x))) (neg eps)) (- (cos (+ x eps)) (cos x)) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (* eps (cos x)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (* 1/6 eps) (* 1/6 x) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)))

simplify168.0ms (1.1%)

Memory

-35.2MiB live, 80.2MiB allocated; 53ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	554	2551
1	2033	2477
0	8520	2244

Stop Event

1×	iter limit
1×	node limit

Counts

146 → 144

Calls

Call 1

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

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 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 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 eps eps) #s(literal 1/4 binary64) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 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 eps) x) 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 (.f64 (.f64 (.f64 eps eps) x) x) #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 (.f64 (.f64 eps eps) x) x) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) x (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) (*.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 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.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 (* 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)
(* 1/2 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))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) x) eps (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (fma.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)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (fma.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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (fma.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 (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (fma.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 #s(literal 1/6 binary64) eps) eps) x (.f64 (fma.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)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 #s(literal 1/6 binary64) eps) eps)) x (.f64 (fma.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 (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64))) x (.f64 (.f64 #s(literal 1/6 binary64) eps) eps)) x (.f64 (fma.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 #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 (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)
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps)
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(- (* 1/24 (pow eps 2)) 1/2)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(fma.f64 (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps #s(literal -1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) eps (.f64 #s(literal -1/36 binary64) x)) eps #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(sin x)
(sin.f64 x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1/4 (* 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 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/4 binary64) eps (/.f64 #s(literal 1 binary64) x))) x) 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 (- (* 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 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(- (* 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 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
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(*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))
(* (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))) 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 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -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 (/.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 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) 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 #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.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(.f64 (neg.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps) (-.f64 (.f64 #s(literal 1/48 binary64) (.f64 x x)) #s(literal 1/24 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(.f64 (neg.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) x) x (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64)) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(.f64 (neg.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) x) x (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (/.f64 (fma.f64 (neg.f64 x) (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) eps) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (/.f64 x eps) #s(literal 1/48 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/48 binary64) (/.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)) (neg.f64 eps))) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -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))) eps)) (*.f64 eps eps))
(* (pow eps 2) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))

rewrite119.0ms (0.8%)

Memory

0.2MiB live, 45.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	702
0	120	698
1	489	685
0	3846	639

Stop Event

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

Counts

26 → 143

Calls

Call 1

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

Outputs
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 eps) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 eps) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (sin.f64 x) (neg.f64 eps))))
(/.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (neg.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64)))) (neg.f64 (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (sin.f64 x) (neg.f64 eps))) (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64))) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (sin.f64 x) (neg.f64 eps))) (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64))))
(neg.f64 (fma.f64 (sin.f64 x) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps)))
(neg.f64 (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps (*.f64 (sin.f64 x) eps)))
(neg.f64 (.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))))
(fma.f64 (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 (neg.f64 eps) #s(literal 1/2 binary64)) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps)) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 (cos.f64 x) (neg.f64 eps)) (.f64 #s(literal 1/2 binary64) eps) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (neg.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (cos.f64 x) (neg.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 (cos.f64 x) (.f64 (.f64 #s(literal 1/2 binary64) eps) (neg.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))) (neg.f64 eps)))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 x) (neg.f64 eps)) #s(literal 2 binary64)) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) #s(literal 2 binary64)) (.f64 (neg.f64 eps) (-.f64 (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))))
(-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) (neg.f64 eps))))
(-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (neg.f64 (neg.f64 eps)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))))
(-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)) eps))
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(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps) #s(literal 2 binary64)) (fma.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps (sin.f64 x)) (pow.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps (sin.f64 x)) (pow.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps) #s(literal 2 binary64)))))
(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))) eps)
(.f64 eps #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (*.f64 #s(literal 1/6 binary64) x))
(*.f64 #s(literal 1/6 binary64) eps)
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/6 binary64))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64))))
#s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)))

eval91.0ms (0.6%)

Memory: -15.8MiB live, 29.6MiB allocated; 4ms collecting garbage
Compiler: Compiled 16 204 to 1 529 computations (90.6% saved)

prune26.0ms (0.2%)

Memory

29.9MiB live, 29.9MiB allocated; 0ms collecting garbage

Pruning

27 alts after pruning (19 fresh and 8 done)

	Pruned	Kept	Total
New	280	7	287
Fresh	3	12	15
Picked	3	2	5
Done	0	6	6
Total	286	27	313

Accuracy

100.0%

Counts

313 → 27

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))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* eps (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) 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)))
	99.2%	#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)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) #s(approx (* (* (cos x) eps) 1/24) (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x))) 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)))
	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)))
	52.0%	#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)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.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 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
✓	79.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 2 721 to 1 024 computations (62.4% saved)

regimes51.0ms (0.3%)

Memory

-19.4MiB live, 35.8MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

32.0ms	eps
10.0ms	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)

regimes28.0ms (0.2%)

Memory

14.9MiB live, 14.9MiB allocated; 0ms 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 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)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* eps (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps))) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #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)))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) (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)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))) #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 (/.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)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))

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

Calls

3 calls:

9.0ms	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)

regimes32.0ms (0.2%)

Memory

-33.4MiB live, 13.5MiB allocated; 1ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

15.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated; 0ms collecting garbage

Counts

34 → 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 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)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* eps (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps))) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #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	eps
8.0ms	x
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)

regimes24.0ms (0.2%)

Memory

-24.3MiB live, 21.9MiB allocated; 2ms 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) eps #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 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)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* eps (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps))) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #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(literal 1/2 binary64) #s(approx (* eps (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x x) eps))) (neg.f64 eps))))

Calls

3 calls:

9.0ms	x
7.0ms	eps
6.0ms	(-.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)

regimes20.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

7.0ms	eps
7.0ms	x
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)

regimes18.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) 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 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #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)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#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)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) #s(approx (+ (* (* eps x) 1/6) (- (* (* eps eps) 1/24) 1/2)) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

6.0ms	eps
6.0ms	x
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)

regimes18.0ms (0.1%)

Memory

-34.9MiB live, 12.3MiB allocated; 1ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

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

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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 (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(approx (+ ( (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) (.f64 #s(literal 1/6 binary64) x)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64)) x)))) 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
98.7%	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

11.0MiB live, 11.0MiB 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (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)))

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:

4.0ms	eps
4.0ms	x
3.0ms	(-.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)

regimes12.0ms (0.1%)

Memory

-43.8MiB live, 8.9MiB allocated; 2ms 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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 (-.f64 (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)) eps) x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Outputs

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

Calls

3 calls:

5.0ms	x
3.0ms	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	`x`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms 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 (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (sin x) (neg eps)) (* (* 1/2 (* eps (cos x))) (neg eps))) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* -1/4 (* eps x)) 1) x) (* 1/2 eps)) (.f64 (.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* (+ (* -1/48 (* eps eps)) 1/4) eps)) x) (- (* (* 1/6 eps) eps) 1)) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) x) x) #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 (+ ( (* (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)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

6.7MiB live, 6.7MiB 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

5.4MiB live, 5.4MiB 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

5.4MiB live, 5.4MiB 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)

simplify61.0ms (0.4%)

Memory

-17.5MiB live, 27.9MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	720
1	309	714
2	643	712
3	1828	704
4	6379	704

Stop Event

1×	node limit

Calls

Call 1

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

derivations1.0s (7.1%)

Memory

36.9MiB live, 271.5MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	514	2414
1	1868	2354
0	8059	2132
0	554	2551
1	2033	2477
0	8520	2244
0	6	16
0	10	16
1	62	16
2	615	16
0	8141	16
0	42	268
0	70	256
1	259	252
0	2220	248
0	493	2235
1	1863	2188
2	7542	2178
0	8259	1998
0	105	296
1	308	293
2	814	293
3	2685	292
4	6556	292
0	8099	272

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

Compiler

Compiled 720 to 193 computations (73.2% saved)

preprocess152.0ms (1%)

Memory: -5.1MiB live, 90.4MiB allocated; 19ms collecting garbage
Compiler: Compiled 1 488 to 428 computations (71.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze538.0ms (3.7%)

sample8.4s (57.4%)

explain235.0ms (1.6%)

preprocess250.0ms (1.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify144.0ms (1%)

localize154.0ms (1.1%)

series4.0ms (0%)

simplify141.0ms (1%)

rewrite154.0ms (1.1%)

eval33.0ms (0.2%)

prune8.0ms (0.1%)

simplify168.0ms (1.2%)

localize380.0ms (2.6%)

series41.0ms (0.3%)

simplify165.0ms (1.1%)

rewrite106.0ms (0.7%)

eval50.0ms (0.3%)

prune20.0ms (0.1%)

simplify165.0ms (1.1%)

localize491.0ms (3.4%)

series31.0ms (0.2%)

simplify147.0ms (1%)

rewrite162.0ms (1.1%)

eval43.0ms (0.3%)

prune23.0ms (0.2%)

simplify128.0ms (0.9%)

localize483.0ms (3.3%)

series23.0ms (0.2%)

simplify168.0ms (1.1%)

rewrite119.0ms (0.8%)

eval91.0ms (0.6%)

prune26.0ms (0.2%)

regimes51.0ms (0.3%)

regimes28.0ms (0.2%)

regimes32.0ms (0.2%)

regimes23.0ms (0.2%)

regimes24.0ms (0.2%)

regimes20.0ms (0.1%)

regimes18.0ms (0.1%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify61.0ms (0.4%)

derivations1.0s (7.1%)

preprocess152.0ms (1%)

end0.0ms (0%)

Profiling