Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze36.0ms (0.3%)

Memory

-3.5MiB live, 12.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.2s (58.1%)

Memory

0.2MiB live, 1 709.7MiB allocated

Samples

2.3s	25 800×	0	invalid
2.2s	5 678×	2	valid
386.0ms	2 461×	1	valid
13.0ms	117×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.9s

ival-cos: 1.8s (46.6% of total)

const: 493.0ms (12.7% of total)

adjust: 352.0ms (9.1% of total)

ival-mult: 209.0ms (5.4% of total)

ival-sub: 200.0ms (5.1% of total)

ival-fabs: 179.0ms (4.6% of total)

ival-<=: 175.0ms (4.5% of total)

ival-add: 167.0ms (4.3% of total)

ival-<: 151.0ms (3.9% of total)

ival-and: 94.0ms (2.4% of total)

exact: 42.0ms (1.1% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

explain184.0ms (1.7%)

Memory

-5.0MiB live, 44.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
125	1	(-1.1712060230009836e-161 5.869554393879608e-163)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	126	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	125	0
-	1	130

Precision

0.9920634920634921

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	0	0
-	1	0	130

Precision?

0.9920634920634921

Recall?

1.0

Freqs

test

number	freq
0	130
1	124
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

73.293701171875

Average Time

0.2863035202026367

Samples

124.0ms	356×	2	valid
17.0ms	148×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-cos: 94.0ms (78.1% of total)

adjust: 17.0ms (14.1% of total)

ival-sub: 6.0ms (5% of total)

ival-add: 3.0ms (2.5% of total)

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

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

preprocess24.0ms (0.2%)

Memory

-1.4MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (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: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (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)

localize78.0ms (0.7%)

Memory

4.9MiB live, 12.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.07979192021901796	(cos.f64 (+.f64 x eps))
accuracy	28.310098894319662	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

62.0ms	178×	2	valid
9.0ms	74×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-cos: 47.0ms (77.1% of total)

adjust: 9.0ms (14.8% of total)

ival-sub: 3.0ms (4.9% of total)

ival-add: 2.0ms (3.3% of total)

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

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

series4.0ms (0%)

Memory

-5.8MiB live, 1.8MiB allocated

Counts

4 → 33

Calls

Call 1

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

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

Calls

6 calls:

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

simplify132.0ms (1.2%)

Memory

-2.7MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	277	293
2	609	293
3	2402	292
4	7842	292
0	8510	272

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite146.0ms (1.4%)

Memory

4.0MiB live, 48.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval27.0ms (0.3%)

Memory: 4.3MiB live, 21.6MiB allocated
Compiler: Compiled 6 613 to 894 computations (86.5% saved)

prune7.0ms (0.1%)

Memory

-3.6MiB live, 11.5MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	244	7	251
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	244	8	252

Accuracy

99.8%

Counts

252 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	55.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶	54.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 223 to 176 computations (21.1% saved)

simplify149.0ms (1.4%)

Memory

3.1MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	195
0	55	195
1	92	195
2	156	195
3	246	195
4	374	195
5	609	195
6	1111	195
7	1980	195
8	2472	195
9	2695	195
10	2793	195
11	2844	195
12	2867	195
13	2883	195
14	2899	195
15	2907	195
16	2907	195
17	2907	195
18	2919	195
0	2919	195

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize213.0ms (2%)

Memory

-11.8MiB live, 49.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.07979192021901796	(cos.f64 (+.f64 x eps))
accuracy	0.7129059104343674	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	28.310098894319662	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy	0	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	12.622645992770918	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(+.f64 x eps)
accuracy	0.07979192021901796	(cos.f64 (+.f64 x eps))
accuracy	0.8784769649176744	#s(approx (cos x) #s(literal 1 binary64))
accuracy	28.310098894319662	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 eps)
accuracy	27.858612303195702	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	28.273959949481306	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	0.02572250976844202	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
accuracy	0.12109375	(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)

Samples

151.0ms	178×	2	valid
28.0ms	76×	1	valid
1.0ms	1×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 351 to 61 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-cos: 78.0ms (52.9% of total)

ival-mult: 28.0ms (19% of total)

adjust: 21.0ms (14.2% of total)

ival-add: 7.0ms (4.7% of total)

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

const: 3.0ms (2% of total)

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

ival-neg: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.1%)

Memory

0.7MiB live, 7.8MiB allocated

Counts

19 → 77

Calls

Call 1

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

Outputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 (* 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)))))))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(pow x 2)
(- (cos (+ eps x)) (cos x))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -1 (* eps (sin x)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
-1
(- (* 1/6 (pow eps 2)) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* eps (+ 1 (/ x eps)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (* eps eps) 1/6) -1) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (* x x))
3.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (* eps eps) 1/6) -1) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (* x x))
2.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (* eps eps) 1/6) -1) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (* x x))
2.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (* eps eps) 1/6) -1) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (* x x))
2.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (+ (* (* eps eps) 1/6) -1) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos x) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (cos x) (* x x))

simplify126.0ms (1.2%)

Memory

4.4MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	246	923
1	716	904
2	1989	880
3	5513	880
0	8380	805

Stop Event

1×	iter limit
1×	node limit

Counts

77 → 75

Calls

Call 1

Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 (* 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)))))))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(pow x 2)
(- (cos (+ eps x)) (cos x))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -1 (* eps (sin x)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
-1
(- (* 1/6 (pow eps 2)) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* eps (+ 1 (/ x eps)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))

Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (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)))))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) (.f64 #s(literal 1/4 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(pow x 2)
(*.f64 x x)
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(sin x)
(sin.f64 x)
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(cos x)
(cos.f64 x)
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(- (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)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
-1
#s(literal -1 binary64)
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(* -1 eps)
(neg.f64 eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 eps))
(* 1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)))

rewrite140.0ms (1.3%)

Memory

-2.0MiB live, 54.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	151
0	55	151
1	197	151
2	1372	151
0	8414	151

Stop Event

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

Counts

19 → 357

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))) (pow.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))))))
(.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (fma.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)))))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps))) (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps))) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps))) (neg.f64 (sin.f64 x))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) #s(literal 2 binary64)))) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))))
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eval65.0ms (0.6%)

Memory: 0.6MiB live, 43.3MiB allocated
Compiler: Compiled 17 617 to 1 838 computations (89.6% saved)

prune15.0ms (0.1%)

Memory

-2.8MiB live, 22.1MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	479	9	488
Fresh	1	1	2
Picked	3	2	5
Done	0	1	1
Total	483	13	496

Accuracy

100.0%

Counts

496 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	96.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 eps))) eps))
	55.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
▶	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
▶	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 723 to 498 computations (31.1% saved)

simplify135.0ms (1.3%)

Memory

4.1MiB live, 39.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff	512	(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff	6592	(fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps)))
cost-diff	0	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff	192	(fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
cost-diff	0	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	477
0	97	467
1	193	467
2	501	450
3	1222	443
4	3143	437
5	6004	437
0	8088	421

Stop Event

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

Calls

Call 1

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

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

localize282.0ms (2.7%)

Memory

-3.3MiB live, 79.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps)))
accuracy	0.015625	(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
accuracy	0.02572250976844202	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy	0.9064671253993954	#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0.02572250976844202	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy	0.12109375	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.359375	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.9161713607019323	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.00390625	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
accuracy	0.01171875	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
accuracy	0.6853693292712055	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x))
accuracy	12.622645992770918	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
accuracy	0	(*.f64 (neg.f64 x) eps)
accuracy	0	(neg.f64 x)
accuracy	0.9064620990610578	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	12.622645992770918	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.07326469244564428	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1171875	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

178.0ms	176×	2	valid
44.0ms	74×	1	valid
2.0ms	1×	5	exit
2.0ms	1×	3	valid
2.0ms	4×	0	valid

Compiler

Compiled 803 to 125 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 182.0ms

ival-cos: 54.0ms (29.7% of total)

ival-mult: 48.0ms (26.4% of total)

adjust: 42.0ms (23.1% of total)

ival-add: 19.0ms (10.4% of total)

ival-sin: 6.0ms (3.3% of total)

const: 4.0ms (2.2% of total)

ival-sub: 3.0ms (1.6% of total)

ival-pow: 3.0ms (1.6% of total)

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

exact: 1.0ms (0.5% of total)

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

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

series30.0ms (0.3%)

Memory

0.8MiB live, 15.5MiB allocated

Counts

23 → 128

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) 1/6) -1)) (+ (* (* x x) 1/6) -1) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (+ (* (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps))
5.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) 1/6) -1)) (+ (* (* x x) 1/6) -1) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (+ (* (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps))
5.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) 1/6) -1)) (+ (* (* x x) 1/6) -1) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (+ (* (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps))
4.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) 1/6) -1)) (+ (* (* x x) 1/6) -1) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (+ (* (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps))
4.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* x x) 1/6) -1)) (+ (* (* x x) 1/6) -1) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (+ (* (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) x) (* (* eps eps) -1/2)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps))

simplify149.0ms (1.4%)

Memory

-0.3MiB live, 46.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	454	1900
1	1407	1813
2	4124	1801
0	8391	1661

Stop Event

1×	iter limit
1×	node limit

Counts

128 → 126

Calls

Call 1

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

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

rewrite149.0ms (1.4%)

Memory

-0.2MiB live, 57.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	390
0	97	382
1	367	382
2	3193	371
0	9666	361

Stop Event

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

Counts

23 → 490

Calls

Call 1

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

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

eval68.0ms (0.6%)

Memory: 3.5MiB live, 54.0MiB allocated
Compiler: Compiled 29 582 to 3 095 computations (89.5% saved)

prune23.0ms (0.2%)

Memory

-3.0MiB live, 30.9MiB allocated

Pruning

21 alts after pruning (16 fresh and 5 done)

	Pruned	Kept	Total
New	585	14	599
Fresh	3	2	5
Picked	2	3	5
Done	1	2	3
Total	591	21	612

Accuracy

100.0%

Counts

612 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	84.9%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 eps #s(literal -1/2 binary64) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) x)))) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	96.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 eps))) eps))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
▶	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps)))) eps))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (.f64 (fma.f64 #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))) eps) eps))) eps))
	55.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) eps))) eps))
	54.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) eps (+.f64 eps (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps x) eps) eps)))
	72.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	29.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps #s(approx (+ (* (* x x) 1/6) -1) (.f64 (.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x))) x)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
▶	54.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))

Compiler

Compiled 1 502 to 995 computations (33.8% saved)

simplify189.0ms (1.8%)

Memory

-2.6MiB live, 49.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff	64	(fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
cost-diff	320	(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))
cost-diff	0	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps))))
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps)))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps)))) eps))
cost-diff	1024	(.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps))
cost-diff	0	#s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))
cost-diff	0	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x))))
cost-diff	0	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
cost-diff	0	(*.f64 x eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (*.f64 x eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	818
0	109	812
1	200	812
2	502	808
3	1120	785
4	2957	785
5	5570	775
0	8341	724

Stop Event

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

Calls

Call 1

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

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

localize309.0ms (2.9%)

Memory

2.1MiB live, 95.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.26009750976844204	(fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64)))
accuracy	0.34375	(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))
accuracy	0.6854773104539656	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.12109375	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps)))) eps)
accuracy	0.9161713607019323	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps))))
accuracy	31.62347440012798	(.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps))
accuracy	59.16080499051575	#s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)) (*.f64 eps eps)))
accuracy	0.02572250976844202	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
accuracy	0.12109375	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps)
accuracy	0.14473852351675648	#s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))
accuracy	0.9161713607019323	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x))))
accuracy	0	(*.f64 x eps)
accuracy	12.622645992770918	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))
accuracy	29.37196264950425	#s(approx (* (neg eps) (sin x)) (*.f64 x eps))
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
accuracy	0.015625	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.07326469244564428	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1171875	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))

Samples

197.0ms	175×	2	valid
52.0ms	74×	1	valid
5.0ms	3×	3	valid
2.0ms	4×	0	valid

Compiler

Compiled 1 288 to 147 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 208.0ms

ival-mult: 58.0ms (27.9% of total)

ival-cos: 52.0ms (25.1% of total)

adjust: 46.0ms (22.2% of total)

ival-add: 24.0ms (11.6% of total)

const: 12.0ms (5.8% of total)

ival-sin: 6.0ms (2.9% of total)

ival-div: 4.0ms (1.9% of total)

ival-sub: 3.0ms (1.4% of total)

ival-neg: 2.0ms (1% of total)

exact: 1.0ms (0.5% of total)

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

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

series26.0ms (0.2%)

Memory

7.0MiB live, 14.7MiB allocated

Counts

23 → 129

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* x eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)))
4.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* x eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)))
4.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* x eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)))
3.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* x eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)))
3.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* x eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)))

simplify150.0ms (1.4%)

Memory

0.4MiB live, 47.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	458	1978
1	1449	1905
2	4179	1895
0	8381	1738

Stop Event

1×	iter limit
1×	node limit

Counts

129 → 128

Calls

Call 1

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

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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 (.f64 x x) (pow.f64 (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 (+ (* 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 (.f64 x x) (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)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (.f64 x (.f64 #s(literal -1/2 binary64) x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(fma.f64 (neg.f64 x) (sin.f64 eps) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1 (* 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))
(* eps x)
(*.f64 eps x)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps)) x) #s(literal -1/6 binary64) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 eps))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
(.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps)
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64))
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)
(fma.f64 (.f64 eps x) #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(* 1/4 eps)
(*.f64 #s(literal 1/4 binary64) eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(* 1/4 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) eps)
(* (pow x 2) (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) (*.f64 x x))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))) (/ 1 x)))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) (*.f64 x x))
(* (pow x 2) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)))
(.f64 (.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) eps)) x) x)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) eps))) x) x)
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) x) #s(literal -1/6 binary64))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) x) x)
(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/6 binary64) eps) x) (/.f64 eps x) (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))) (*.f64 x x))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (neg.f64 x))) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (neg.f64 x))) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) (neg.f64 x))) x) x)
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))) x)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2)))
(fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 x))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)
(* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))
(.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
(.f64 x (fma.f64 (.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))
(- (* 1/6 (pow x 2)) 1)
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps (.f64 #s(literal 1/4 binary64) x)) eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) x))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (.f64 eps eps))
(* 1/6 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64))
(* (pow eps 2) (- (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(.f64 (fma.f64 (.f64 x (/.f64 x eps)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (*.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (fma.f64 (.f64 x (/.f64 x eps)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (/.f64 (/.f64 x eps) eps)) (*.f64 eps eps))
(* -1/36 (* (pow eps 2) x))
(.f64 (.f64 #s(literal -1/36 binary64) (*.f64 eps x)) eps)
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) x)) eps) eps)
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps) eps)
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))) eps) eps)
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(.f64 (-.f64 (+.f64 (fma.f64 (.f64 x (/.f64 (/.f64 x eps) eps)) #s(literal 1/6 binary64) (fma.f64 (.f64 #s(literal -1/36 binary64) x) x (.f64 (/.f64 x eps) #s(literal 1/4 binary64)))) #s(literal 1/6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) (*.f64 eps eps))
(* -1/48 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) eps) eps) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps))) eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(.f64 (.f64 (neg.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)))
(.f64 (.f64 (fma.f64 #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))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)) eps) eps)
(* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))
(.f64 (-.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/4 binary64) x (/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) eps) eps) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) (neg.f64 eps))) eps) eps)

rewrite177.0ms (1.7%)

Memory

-2.1MiB live, 65.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	668
0	109	664
1	405	664
2	3639	664
0	9469	631

Stop Event

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

Counts

23 → 318

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
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(/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x)) (.f64 eps eps) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal 1 binary64)) (.f64 #s(literal 1/4 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal 1 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x)) (neg.f64 eps) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/4 binary64)))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (neg.f64 eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x)) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/4 binary64)))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x)) (neg.f64 eps) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 #s(literal 1/4 binary64) (neg.f64 (.f64 eps eps))))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (neg.f64 eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x)) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 #s(literal 1/4 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (*.f64 eps eps)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) #s(literal 2 binary64)) (.f64 #s(literal 1/16 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (*.f64 #s(literal 1/4 binary64) eps)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (.f64 #s(literal 1/4 binary64) eps))))))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (.f64 #s(literal 1/4 binary64) eps)))) (fma.f64 #s(literal -1/216 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal 3 binary64)))))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (.f64 (.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal -1/6 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (.f64 #s(literal 1/4 binary64) eps)))))
(fma.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 (.f64 #s(literal -1/6 binary64) x) (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) (.f64 #s(literal -1/6 binary64) x) (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))
(fma.f64 eps #s(literal 1/4 binary64) (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))
(fma.f64 x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 #s(literal 1/4 binary64) eps))
(-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) (/.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))))
(+.f64 (.f64 #s(literal 1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))
(+.f64 (.f64 #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)) (.f64 #s(literal 1/4 binary64) eps))

eval55.0ms (0.5%)

Memory: 0.3MiB live, 43.8MiB allocated
Compiler: Compiled 28 924 to 2 476 computations (91.4% saved)

prune23.0ms (0.2%)

Memory

1.7MiB live, 27.8MiB allocated

Pruning

22 alts after pruning (16 fresh and 6 done)

	Pruned	Kept	Total
New	419	10	429
Fresh	5	6	11
Picked	3	2	5
Done	1	4	5
Total	428	22	450

Accuracy

100.0%

Counts

450 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	80.3%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ (* 2 x) eps))) (sin.f64 x)) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps #s(approx (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6) (.f64 #s(literal 1/6 binary64) x))) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) eps) eps)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* 1/4 eps) (* (* (+ (* (* eps eps) 1/6) -1) x) -1/6)) x) (+ (* (* eps eps) 1/6) -1)) (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) eps)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	96.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) eps) (neg.f64 eps))) eps))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
	55.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) (.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) eps))) eps))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) #s(approx (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)))) eps))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) #s(approx (+ (* (+ (* eps (+ (* 1/4 x) (* 1/6 eps))) -1) x) (* -1/2 eps)) #s(approx (* (+ (* 1/6 x) (/ (+ (* 1/4 (* x x)) -1/2) eps)) (* eps eps)) (.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps)))) eps))
	54.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) eps (+.f64 eps (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64)))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (* 1/4 x) (* eps eps)) (+ (* (pow eps 3) 1/6) (neg eps))) (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps x) eps) eps)))
	72.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
✓	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
✓	54.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))

Compiler

Compiled 2 633 to 928 computations (64.8% saved)

regimes29.0ms (0.3%)

Memory

0.0MiB live, 15.3MiB allocated

Counts

41 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	eps
10.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.3%)

Memory

-1.3MiB live, 14.9MiB allocated

Counts

39 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.7%	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)

regimes24.0ms (0.2%)

Memory

-1.9MiB live, 13.1MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

0.8MiB live, 11.1MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

1.9MiB live, 9.6MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-7.1MiB live, 8.7MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

-2.3MiB live, 6.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.7%	1	`x`
79.7%	1	`eps`
79.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

-2.5MiB live, 5.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.7%	1	`x`
79.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
54.1%	1	`x`
54.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
54.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify24.0ms (0.2%)

Memory

-4.8MiB live, 19.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	419
1	133	419
2	140	419
3	145	419
4	148	419
5	149	419

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (10.2%)

Memory

2.0MiB live, 9.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	390
0	97	382
1	367	382
2	3193	371
0	9666	361
0	454	1900
1	1407	1813
2	4124	1801
0	8391	1661
0	246	923
1	716	904
2	1989	880
3	5513	880
0	8380	805
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	105	296
1	277	293
2	609	293
3	2402	292
4	7842	292
0	8510	272
0	458	1978
1	1449	1905
2	4179	1895
0	8381	1738

Stop Event

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

Compiler

Compiled 500 to 225 computations (55% saved)

preprocess56.0ms (0.5%)

Memory: 0.4MiB live, 37.8MiB allocated
Compiler: Compiled 886 to 276 computations (68.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze36.0ms (0.3%)

sample6.2s (58.1%)

explain184.0ms (1.7%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize78.0ms (0.7%)

series4.0ms (0%)

simplify132.0ms (1.2%)

rewrite146.0ms (1.4%)

eval27.0ms (0.3%)

prune7.0ms (0.1%)

simplify149.0ms (1.4%)

localize213.0ms (2%)

series15.0ms (0.1%)

simplify126.0ms (1.2%)

rewrite140.0ms (1.3%)

eval65.0ms (0.6%)

prune15.0ms (0.1%)

simplify135.0ms (1.3%)

localize282.0ms (2.7%)

series30.0ms (0.3%)

simplify149.0ms (1.4%)

rewrite149.0ms (1.4%)

eval68.0ms (0.6%)

prune23.0ms (0.2%)

simplify189.0ms (1.8%)

localize309.0ms (2.9%)

series26.0ms (0.2%)

simplify150.0ms (1.4%)

rewrite177.0ms (1.7%)

eval55.0ms (0.5%)

prune23.0ms (0.2%)

regimes29.0ms (0.3%)

regimes28.0ms (0.3%)

regimes24.0ms (0.2%)

regimes20.0ms (0.2%)

regimes16.0ms (0.1%)

regimes14.0ms (0.1%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify24.0ms (0.2%)

soundness1.1s (10.2%)

preprocess56.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18