Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze191.0ms (1.3%)

Memory

2.0MiB live, 75.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.9s (66%)

Memory

-61.6MiB live, 9 011.9MiB allocated

Samples

4.1s	26 276×	0	invalid
3.1s	5 644×	2	valid
526.0ms	2 483×	1	valid
18.0ms	129×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.8s

ival-cos: 2.3s (39.3% of total)

const: 976.0ms (16.7% of total)

adjust: 472.0ms (8.1% of total)

ival-sub: 436.0ms (7.5% of total)

ival-fabs: 385.0ms (6.6% of total)

ival-mult: 324.0ms (5.5% of total)

ival-add: 275.0ms (4.7% of total)

ival-<: 267.0ms (4.6% of total)

ival-<=: 245.0ms (4.2% of total)

ival-and: 108.0ms (1.8% of total)

exact: 46.0ms (0.8% of total)

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

Bogosity

explain294.0ms (2%)

Memory

-19.6MiB live, 194.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
133	1	(2.3444364319679304e-157 1.8835784759284745e-166)	-	`(-.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	134	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	133	0
-	1	122

Precision

0.9925373134328358

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	0
-	1	0	122

Precision?

0.9925373134328358

Recall?

1.0

Freqs

test

number	freq
0	122
1	132
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

166.0ms	338×	2	valid
46.0ms	172×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

ival-cos: 117.0ms (80.1% of total)

adjust: 19.0ms (13% of total)

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

ival-add: 3.0ms (2.1% of total)

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

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

preprocess24.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB 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
▶	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize91.0ms (0.6%)

Memory

15.0MiB live, 89.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.06310475823848478	(cos.f64 (+.f64 x eps))
accuracy	30.201135029810292	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

71.0ms	169×	2	valid
14.0ms	86×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-cos: 55.0ms (76.1% of total)

adjust: 9.0ms (12.5% of total)

ival-sub: 6.0ms (8.3% of total)

ival-add: 2.0ms (2.8% of total)

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

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

series4.0ms (0%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

4 → 33

Calls

Call 1

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

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

Calls

6 calls:

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

simplify136.0ms (0.9%)

Memory

-14.7MiB live, 139.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite171.0ms (1.1%)

Memory

7.4MiB live, 205.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval44.0ms (0.3%)

Memory: -15.2MiB live, 68.3MiB allocated
Compiler: Compiled 6 613 to 893 computations (86.5% saved)

prune6.0ms (0%)

Memory

19.1MiB live, 19.1MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	245	6	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	246	6	252

Accuracy

99.8%

Counts

252 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
▶	52.0%	(-.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))
▶	51.9%	#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 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	81.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))

Compiler

Compiled 176 to 138 computations (21.6% saved)

simplify108.0ms (0.7%)

Memory

0.9MiB live, 39.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	189
0	51	189
1	82	189
2	130	189
3	234	189
4	330	189
5	446	189
6	674	189
7	969	189
8	1358	189
9	1487	189
10	1576	189
11	1729	189
12	2020	189
13	2535	189
14	2717	189
15	2765	189
16	2778	189
17	2778	189
18	2778	189
19	2778	189
20	2781	189
0	2781	189

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize256.0ms (1.7%)

Memory

-27.3MiB live, 330.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.06310475823848478	(cos.f64 (+.f64 x eps))
accuracy	0.8568843573976235	#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	30.201135029810292	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0.0	(*.f64 (neg.f64 (sin.f64 x)) eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(neg.f64 (sin.f64 x))
accuracy	11.905107270865678	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
accuracy	0.0	(+.f64 x eps)
accuracy	0.06310475823848478	(cos.f64 (+.f64 x eps))
accuracy	1.3110247037261888	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.201135029810292	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.0	(cos.f64 eps)
accuracy	30.039702186130363	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	30.066029541218906	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.00390625	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
accuracy	0.01171875	(-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x))
accuracy	0.13671875	(.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)

Samples

152.0ms	170×	2	valid
40.0ms	85×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 143 to 25 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-cos: 79.0ms (51.7% of total)

adjust: 24.0ms (15.7% of total)

ival-mult: 23.0ms (15.1% of total)

ival-sub: 10.0ms (6.5% of total)

ival-add: 7.0ms (4.6% of total)

const: 4.0ms (2.6% of total)

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

ival-neg: 2.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

18 → 74

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* 1/24 (* x x)) -1/2))
2.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (- (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 (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* 1/24 (* x x)) -1/2))
2.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (- (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 (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* 1/24 (* x x)) -1/2))
2.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (- (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 (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* 1/24 (* x x)) -1/2))
2.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (- (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 (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* 1/24 (* x x)) -1/2))

simplify216.0ms (1.4%)

Memory

17.5MiB live, 135.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	241	787
1	688	777
2	1772	754
3	4451	753
0	8199	689

Stop Event

1×	iter limit
1×	node limit

Counts

74 → 72

Calls

Call 1

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

rewrite200.0ms (1.3%)

Memory

-18.5MiB live, 139.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	145
0	51	145
1	189	145
2	1292	145
0	8222	145

Stop Event

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

Counts

18 → 342

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))) #s(literal -1 binary64)))
(.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (pow.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))

eval101.0ms (0.7%)

Memory: -15.5MiB live, 84.3MiB allocated
Compiler: Compiled 16 744 to 1 783 computations (89.4% saved)

prune30.0ms (0.2%)

Memory

-2.2MiB live, 37.5MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	457	16	473
Fresh	0	1	1
Picked	3	2	5
Done	0	0	0
Total	460	19	479

Accuracy

100.0%

Counts

479 → 19

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))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))
	39.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x))))) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) x) x (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (neg.f64 (sin.f64 x))))) eps))
✓	81.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
▶	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
▶	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
▶	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) 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)))
	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 976 to 664 computations (32% saved)

simplify161.0ms (1.1%)

Memory

11.2MiB live, 167.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	404
0	73	396
1	122	396
2	210	396
3	472	388
4	1084	388
5	2020	388
6	3828	388
7	5432	388
8	7293	388
0	8020	387

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps) (sin.f64 x)) (neg.f64 eps)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps) (sin.f64 x)) (neg.f64 eps))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 x)
x
eps
(*.f64 (neg.f64 (sin.f64 x)) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 (sin.f64 x))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
#s(approx (neg (sin x)) (neg.f64 x))
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps)
(*.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x))
#s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64))
(fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))
#s(literal -1/120 binary64)
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
(*.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x))
#s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps) (sin.f64 x)) (neg.f64 eps)))
(/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps) (sin.f64 x)) (neg.f64 eps))
eps
(/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x)))
#s(literal 1 binary64)
(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize275.0ms (1.8%)

Memory

13.2MiB live, 455.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))
accuracy	0.01171875	(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))
accuracy	0.140625	(/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
accuracy	0.00390625	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
accuracy	0.7775642833255525	#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x))
accuracy	11.905107270865678	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
accuracy	0.0078125	(.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)
accuracy	0.01171875	(fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))
accuracy	0.8148827349343908	#s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x))
accuracy	11.905107270865678	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
accuracy	0.0	(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
accuracy	0.0	(neg.f64 x)
accuracy	1.1993830613037402	#s(approx (neg (sin x)) (neg.f64 x))
accuracy	11.905107270865678	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
accuracy	0.1171875	(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))

Samples

168.0ms	168×	2	valid
51.0ms	85×	1	valid
2.0ms	1×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 267 to 38 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 174.0ms

ival-cos: 51.0ms (29.4% of total)

ival-mult: 38.0ms (21.9% of total)

adjust: 30.0ms (17.3% of total)

const: 16.0ms (9.2% of total)

ival-add: 15.0ms (8.6% of total)

ival-div: 8.0ms (4.6% of total)

ival-sub: 7.0ms (4% of total)

ival-sin: 4.0ms (2.3% of total)

ival-neg: 3.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.2%)

Memory

-8.7MiB live, 29.4MiB allocated

Counts

23 → 85

Calls

Call 1

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

Outputs
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(/ -2 eps)
(- (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))
(- (* x (+ (* -1 (* x (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(- (* x (+ (* x (- (* x (- (* 4/3 (/ 1 (pow eps 2))) (* -2 (/ (+ (/ 1 eps) (* 8 (/ 1 (pow eps 3)))) eps)))) (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
1
(+ 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)))
1/6
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* eps (cos x)))
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(cos x)
(* -1/120 (pow x 2))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* 1/5040 (pow x 4))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (- (* 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))
(- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(- (* eps (- (* -1/4 (/ (* eps (pow (cos x) 2)) (pow (sin x) 3))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(- (* eps (- (* eps (- (* 1/8 (/ (* eps (pow (cos x) 3)) (pow (sin x) 4))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(/ -2 (* eps (cos x)))
(/ (- (* 4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps)
(/ (- (* -8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x))))) eps)
(/ (- (* 16 (/ (pow (sin x) 3) (* (pow eps 3) (pow (cos x) 4)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (+ (* 8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (* 2 (/ 1 (cos x)))))) eps)
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (/ (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -8 (/ (pow (sin x) 2) (* eps (pow (cos x) 3)))) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -16 (/ (pow (sin x) 3) (* eps (pow (cos x) 4)))) (* -8 (/ (pow (sin x) 2) (pow (cos x) 3)))) eps)) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (* (+ (* (+ (* -1/120 (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (/ eps (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x)))) (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x))) (- (cos (+ x eps)) (cos x)) (- (* (* -1/2 (cos x)) eps) (sin x)) (cos x) (+ (* -1/120 (* x x)) 1/6) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6))
3.0ms	x	@	-inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (* (+ (* (+ (* -1/120 (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (/ eps (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x)))) (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x))) (- (cos (+ x eps)) (cos x)) (- (* (* -1/2 (cos x)) eps) (sin x)) (cos x) (+ (* -1/120 (* x x)) 1/6) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6))
2.0ms	x	@	0	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (* (+ (* (+ (* -1/120 (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (/ eps (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x)))) (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x))) (- (cos (+ x eps)) (cos x)) (- (* (* -1/2 (cos x)) eps) (sin x)) (cos x) (+ (* -1/120 (* x x)) 1/6) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6))
2.0ms	eps	@	0	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (* (+ (* (+ (* -1/120 (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (/ eps (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x)))) (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x))) (- (cos (+ x eps)) (cos x)) (- (* (* -1/2 (cos x)) eps) (sin x)) (cos x) (+ (* -1/120 (* x x)) 1/6) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6))
2.0ms	eps	@	inf	((+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (- (cos (+ x eps)) (cos x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (* (+ (* (+ (* -1/120 (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) x) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (/ eps (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x)))) (/ 1 (- (* (* -1/2 (cos x)) eps) (sin x))) (- (cos (+ x eps)) (cos x)) (- (* (* -1/2 (cos x)) eps) (sin x)) (cos x) (+ (* -1/120 (* x x)) 1/6) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6))

simplify154.0ms (1%)

Memory

3.7MiB live, 197.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	353	1217
1	1007	1191
2	2906	1166
0	8695	1098

Stop Event

1×	iter limit
1×	node limit

Counts

85 → 85

Calls

Call 1

Inputs
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(/ -2 eps)
(- (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))
(- (* x (+ (* -1 (* x (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(- (* x (+ (* x (- (* x (- (* 4/3 (/ 1 (pow eps 2))) (* -2 (/ (+ (/ 1 eps) (* 8 (/ 1 (pow eps 3)))) eps)))) (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
1
(+ 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)))
1/6
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* eps (cos x)))
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(cos x)
(* -1/120 (pow x 2))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* 1/5040 (pow x 4))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (- (* 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))
(- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(- (* eps (- (* -1/4 (/ (* eps (pow (cos x) 2)) (pow (sin x) 3))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(- (* eps (- (* eps (- (* 1/8 (/ (* eps (pow (cos x) 3)) (pow (sin x) 4))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(/ -2 (* eps (cos x)))
(/ (- (* 4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps)
(/ (- (* -8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x))))) eps)
(/ (- (* 16 (/ (pow (sin x) 3) (* (pow eps 3) (pow (cos x) 4)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (+ (* 8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (* 2 (/ 1 (cos x)))))) eps)
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (/ (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -8 (/ (pow (sin x) 2) (* eps (pow (cos x) 3)))) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -16 (/ (pow (sin x) 3) (* eps (pow (cos x) 4)))) (* -8 (/ (pow (sin x) 2) (pow (cos x) 3)))) eps)) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))

Outputs
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) x) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 (neg.f64 x) eps))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/6 (pow x 2)) 1))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)
(/ -2 eps)
(/.f64 #s(literal -2 binary64) eps)
(- (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))
(fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 eps eps)) x (/.f64 #s(literal -2 binary64) eps))
(- (* x (+ (* -1 (* x (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 eps eps)) (fma.f64 (/.f64 x (pow.f64 eps #s(literal 3 binary64))) #s(literal 8 binary64) (/.f64 x eps))) x (/.f64 #s(literal -2 binary64) eps))
(- (* x (+ (* x (- (* x (- (* 4/3 (/ 1 (pow eps 2))) (* -2 (/ (+ (/ 1 eps) (* 8 (/ 1 (pow eps 3)))) eps)))) (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 4/3 binary64) (.f64 eps eps)) (/.f64 (-.f64 (/.f64 #s(literal -16 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) eps)) eps)) x (-.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal 8 binary64) (pow.f64 eps #s(literal 3 binary64))))) x (/.f64 #s(literal 4 binary64) (.f64 eps eps))) x (/.f64 #s(literal -2 binary64) eps))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
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))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* -1/120 (pow x 2)))
(fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))
(+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))
(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))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1/120 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 1/5040 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/5040 binary64))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 7 binary64)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))
(cos x)
(cos.f64 x)
(* -1/120 (pow x 2))
(.f64 #s(literal -1/120 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) x) x)
(* 1/5040 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/5040 binary64))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 7 binary64)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(/ -1 (sin x))
(/.f64 #s(literal -1 binary64) (sin.f64 x))
(- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(fma.f64 (*.f64 (cos.f64 x) (/.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(- (* eps (- (* -1/4 (/ (* eps (pow (cos x) 2)) (pow (sin x) 3))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(- (* eps (- (* eps (- (* 1/8 (/ (* eps (pow (cos x) 3)) (pow (sin x) 4))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) eps (/.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(/ -2 (* eps (cos x)))
(/.f64 (/.f64 #s(literal -2 binary64) (cos.f64 x)) eps)
(/ (- (* 4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps)
(/.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 #s(literal -2 binary64) (cos.f64 x))) eps)
(/ (- (* -8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x))))) eps)
(/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 #s(literal 4 binary64) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (/.f64 #s(literal 2 binary64) (cos.f64 x))) eps)
(/ (- (* 16 (/ (pow (sin x) 3) (* (pow eps 3) (pow (cos x) 4)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (+ (* 8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (* 2 (/ 1 (cos x)))))) eps)
(/.f64 (fma.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (/.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 #s(literal 4 binary64) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (/.f64 #s(literal 2 binary64) (cos.f64 x)))) eps)
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (/ (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps))
(/.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 #s(literal -2 binary64) (cos.f64 x))) eps)
(* -1 (/ (+ (* -1 (/ (- (* -8 (/ (pow (sin x) 2) (* eps (pow (cos x) 3)))) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 #s(literal 4 binary64) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (/.f64 #s(literal 2 binary64) (cos.f64 x))) eps)
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -16 (/ (pow (sin x) 3) (* eps (pow (cos x) 4)))) (* -8 (/ (pow (sin x) 2) (pow (cos x) 3)))) eps)) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 4 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -16 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 8 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 eps))) eps) (/.f64 #s(literal 2 binary64) (cos.f64 x))) eps)
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))

rewrite168.0ms (1.1%)

Memory

-5.9MiB live, 152.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	321
0	73	313
1	259	313
2	1727	313
0	9108	313

Stop Event

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

Counts

23 → 580

Calls

Call 1

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

Outputs
(.f64 (/.f64 eps (pow.f64 (-.f64 (pow.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))) (pow.f64 (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (/.f64 eps (pow.f64 (-.f64 (pow.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))) #s(literal -1 binary64)))
(.f64 (/.f64 eps (pow.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) eps) (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) eps)) (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x)))))
(.f64 (/.f64 eps #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x)))) #s(literal -1 binary64)))
(.f64 (/.f64 eps #s(literal -1 binary64)) (neg.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x)))))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64))) (pow.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)) (pow.f64 (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (neg.f64 eps) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 eps #s(literal -1 binary64)) (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x)))))
(.f64 (.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps) #s(literal 1 binary64))
(.f64 eps (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))))
(pow.f64 (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) eps)) (-.f64 (pow.f64 (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)) (pow.f64 (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64))) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (pow.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal -1 binary64)) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal -1 binary64)) eps) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x)) (*.f64 (sin.f64 x) eps)))))
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(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)))
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(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/36 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/36 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)))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64)) (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/36 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/36 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/36 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (.f64 x #s(literal 1/6 binary64)))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/36 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/36 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) (.f64 x #s(literal 1/6 binary64)))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64)))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x #s(literal 1/6 binary64))
(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 x (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) #s(literal 1/6 binary64))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x))) (/.f64 (.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x))))
(-.f64 (/.f64 (.f64 (pow.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 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))) (/.f64 #s(literal 1/36 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))))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x))

eval76.0ms (0.5%)

Memory: -17.2MiB live, 65.5MiB allocated
Compiler: Compiled 19 081 to 2 519 computations (86.8% saved)

prune22.0ms (0.1%)

Memory

33.0MiB live, 33.0MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	500	9	509
Fresh	4	8	12
Picked	2	3	5
Done	0	2	2
Total	506	22	528

Accuracy

100.0%

Counts

528 → 22

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))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
▶	100.0%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) x) x (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
✓	81.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
▶	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
✓	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
✓	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) 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)))
	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 1 095 to 738 computations (32.6% saved)

simplify401.0ms (2.7%)

Memory

-40.9MiB live, 125.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	471
0	91	459
1	169	457
2	321	448
3	669	448
4	1266	448
5	2162	448
6	4306	448
7	5400	448
8	6130	448
9	6347	448
10	6408	448
11	6487	448
12	7015	448
13	7253	448
14	7281	448
15	7295	448
16	7305	448
17	7313	448
18	7317	448
19	7317	448
20	7987	448
0	8299	448

Stop Event

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

Calls

Call 1

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

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

localize264.0ms (1.8%)

Memory

7.8MiB live, 83.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps)
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
accuracy	0.1171875	(fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps))
accuracy	0.8860778679208301	#s(approx (* -1/2 (cos x)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
accuracy	0.1171875	(.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)))
accuracy	0.12890625	(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
accuracy	0.38119125976844204	(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))
accuracy	0.8800110641016794	#s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
accuracy	0.13671875	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.1796875	(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
accuracy	0.33203125	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.8763531109860923	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) eps)
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
accuracy	0.13671875	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy	59.14834387877364	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.00390625	(.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
accuracy	0.0078125	(.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
accuracy	0.0078125	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)))
accuracy	0.015625	(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps))

Samples

168.0ms	168×	2	valid
51.0ms	85×	1	valid
2.0ms	1×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 297 to 46 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-mult: 54.0ms (30.7% of total)

ival-cos: 47.0ms (26.7% of total)

adjust: 35.0ms (19.9% of total)

ival-add: 19.0ms (10.8% of total)

ival-sub: 7.0ms (4% of total)

const: 7.0ms (4% of total)

ival-neg: 4.0ms (2.3% of total)

ival-sin: 3.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series21.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

27 → 90

Calls

Call 1

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

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

Calls

6 calls:

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

simplify141.0ms (0.9%)

Memory

12.1MiB live, 47.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	310	1166
1	960	1090
2	2833	1050
0	8026	964

Stop Event

1×	iter limit
1×	node limit

Counts

90 → 89

Calls

Call 1

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

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

rewrite195.0ms (1.3%)

Memory

-12.7MiB live, 69.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	404
0	91	392
1	345	390
2	2493	390
0	9546	390

Stop Event

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

Counts

27 → 416

Calls

Call 1

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

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

eval54.0ms (0.4%)

Memory: 4.6MiB live, 41.8MiB allocated
Compiler: Compiled 24 586 to 2 275 computations (90.7% saved)

prune22.0ms (0.1%)

Memory

-11.9MiB live, 27.9MiB allocated

Pruning

24 alts after pruning (15 fresh and 9 done)

	Pruned	Kept	Total
New	472	4	476
Fresh	1	11	12
Picked	1	4	5
Done	0	5	5
Total	474	24	498

Accuracy

100.0%

Counts

498 → 24

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))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
✓	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) x) x (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x)) eps))
✓	81.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
✓	53.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps))) eps))
	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
✓	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
✓	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
✓	80.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (fma.f64 (neg.f64 x) eps (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
	80.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) 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)))
	80.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 1 718 to 729 computations (57.6% saved)

regimes24.0ms (0.2%)

Memory

13.9MiB live, 13.9MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.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)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) 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)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/4 eps) (* 1/6 x)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #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 (+ (* (* (* -1/2 (cos x)) eps) eps) (* (neg (sin x)) eps)) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (fma.f64 (neg.f64 x) eps (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x) x (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) x) x (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx ( -1/2 (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(-.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)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps (*.f64 (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 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x))))) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (neg.f64 (sin.f64 x))))) eps))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) 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
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	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)

regimes35.0ms (0.2%)

Memory

-36.7MiB live, 11.8MiB allocated

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

22.0ms	x
7.0ms	eps
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes12.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`
97.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Accuracy

Total -17.4b remaining (-137.4%)

Threshold costs -17.4b (-137.4%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
80.2%	1	`x`
80.2%	1	`eps`
80.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify72.0ms (0.5%)

Memory

-27.3MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	218
1	106	218
2	155	218
3	201	218
4	279	218
5	474	218
6	1840	218
7	4373	218

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness887.0ms (5.9%)

Memory

8.3MiB live, 8.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	404
0	91	392
1	345	390
2	2493	390
0	9546	390
0	44	321
0	73	313
1	259	313
2	1727	313
0	9108	313
0	241	787
1	688	777
2	1772	754
3	4451	753
0	8199	689
0	31	145
0	51	145
1	189	145
2	1292	145
0	8222	145
0	105	296
1	277	293
2	628	293
3	2426	292
0	8397	272
0	353	1217
1	1007	1191
2	2906	1166
0	8695	1098

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×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 444 to 245 computations (44.8% saved)

preprocess123.0ms (0.8%)

Memory: -6.4MiB live, 32.2MiB allocated
Compiler: Compiled 496 to 182 computations (63.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

start0.0ms (0%)

analyze191.0ms (1.3%)

sample9.9s (66%)

explain294.0ms (2%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize91.0ms (0.6%)

series4.0ms (0%)

simplify136.0ms (0.9%)

rewrite171.0ms (1.1%)

eval44.0ms (0.3%)

prune6.0ms (0%)

simplify108.0ms (0.7%)

localize256.0ms (1.7%)

series14.0ms (0.1%)

simplify216.0ms (1.4%)

rewrite200.0ms (1.3%)

eval101.0ms (0.7%)

prune30.0ms (0.2%)

simplify161.0ms (1.1%)

localize275.0ms (1.8%)

series23.0ms (0.2%)

simplify154.0ms (1%)

rewrite168.0ms (1.1%)

eval76.0ms (0.5%)

prune22.0ms (0.1%)

simplify401.0ms (2.7%)

localize264.0ms (1.8%)

series21.0ms (0.1%)

simplify141.0ms (0.9%)

rewrite195.0ms (1.3%)

eval54.0ms (0.4%)

prune22.0ms (0.1%)

regimes24.0ms (0.2%)

regimes20.0ms (0.1%)

regimes35.0ms (0.2%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify72.0ms (0.5%)

soundness887.0ms (5.9%)

preprocess123.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18