Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze90.0ms (0.7%)

Memory

-39.7MiB live, 151.8MiB 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)

sample8.9s (65.8%)

Memory

-38.4MiB live, 8 381.8MiB allocated

Samples

3.4s	5 738×	2	valid
3.3s	25 820×	0	invalid
522.0ms	2 461×	1	valid
8.0ms	57×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.2s

ival-cos: 2.2s (42.8% of total)

const: 703.0ms (13.6% of total)

adjust: 461.0ms (8.9% of total)

ival-add: 392.0ms (7.6% of total)

ival-mult: 284.0ms (5.5% of total)

ival-<=: 275.0ms (5.3% of total)

ival-sub: 259.0ms (5% of total)

ival-fabs: 228.0ms (4.4% of total)

ival-<: 189.0ms (3.7% of total)

ival-and: 110.0ms (2.1% of total)

exact: 48.0ms (0.9% of total)

ival-assert: 15.0ms (0.3% of total)

Bogosity

explain226.0ms (1.7%)

Memory

9.8MiB live, 338.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
139	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	139	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	139	0
-	0	117

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	0
-	0	0	117

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	117
1	137
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

149.0ms	352×	2	valid
26.0ms	160×	1	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-cos: 107.0ms (73.1% of total)

adjust: 28.0ms (19.1% of total)

ival-sub: 7.0ms (4.8% of total)

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

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

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

preprocess23.0ms (0.2%)

Memory

6.8MiB live, 49.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	46	41
2	86	41
3	116	41
4	118	41
0	6	7
0	10	7
1	22	7
2	40	7
3	64	7
4	71	7
0	71	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	22	18
2	40	18
3	64	18
4	71	18
0	71	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize101.0ms (0.7%)

Memory

-14.8MiB live, 85.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.057992109428145255	(cos.f64 (+.f64 x eps))
accuracy	31.731272656244137	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

80.0ms	176×	2	valid
11.0ms	80×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-cos: 60.0ms (76.5% of total)

adjust: 12.0ms (15.3% of total)

ival-sub: 3.0ms (3.8% of total)

ival-add: 2.0ms (2.5% of total)

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

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

series4.0ms (0%)

Memory

2.1MiB live, 2.1MiB 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))

simplify119.0ms (0.9%)

Memory

-5.3MiB live, 86.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	308	293
2	779	293
3	2454	292
4	6244	292
0	8035	272

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite161.0ms (1.2%)

Memory

8.6MiB live, 100.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 138

Calls

Call 1

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

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

eval20.0ms (0.1%)

Memory: 27.2MiB live, 27.2MiB allocated
Compiler: Compiled 4 780 to 715 computations (85% saved)

prune9.0ms (0.1%)

Memory

-34.1MiB live, 11.3MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Accuracy

99.9%

Counts

162 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	49.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
▶	99.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
▶	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 245 to 186 computations (24.1% saved)

simplify179.0ms (1.3%)

Memory

-1.0MiB live, 100.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	250
0	60	250
1	109	250
2	226	250
3	585	250
4	1367	250
5	2800	250
6	4954	250
7	7765	250
0	8048	250

Stop Event

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

Calls

Call 1

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

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

localize281.0ms (2.1%)

Memory

2.2MiB live, 286.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
accuracy	0.07847255168572895	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
accuracy	0.10546875	(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(neg.f64 eps)
accuracy	0.00390625	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	13.262510301317853	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0.0	(+.f64 x eps)
accuracy	0.057992109428145255	(cos.f64 (+.f64 x eps))
accuracy	0.8892514742550182	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.731272656244137	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.0	(cos.f64 eps)
accuracy	31.0864756782469	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	31.323975981462915	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.015625	(-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x))
accuracy	0.1015625	(.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.16796875	(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))
accuracy	0.390625	(*.f64 #s(literal 1/24 binary64) eps)

Samples

199.0ms	177×	2	valid
47.0ms	79×	1	valid

Compiler

Compiled 213 to 32 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 185.0ms

ival-cos: 71.0ms (38.3% of total)

adjust: 40.0ms (21.6% of total)

ival-mult: 36.0ms (19.4% of total)

ival-add: 17.0ms (9.2% of total)

ival-sub: 10.0ms (5.4% of total)

const: 7.0ms (3.8% of total)

ival-sin: 4.0ms (2.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory

1.9MiB live, 48.7MiB allocated

Counts

21 → 109

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x))
(.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(*.f64 (cos.f64 x) eps)
(*.f64 #s(literal 1/24 binary64) eps)
(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 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)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(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)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -1 (* eps (sin x)))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* 1/6 (* eps (sin x)))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 eps)
(* 1/24 eps)
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* eps (+ 1 (/ x eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* 1/24 eps) (* (* (sin x) eps) 1/6))
4.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* 1/24 eps) (* (* (sin x) eps) 1/6))
4.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* 1/24 eps) (* (* (sin x) eps) 1/6))
3.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* 1/24 eps) (* (* (sin x) eps) 1/6))
3.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (* 1/24 eps) (* (* (sin x) eps) 1/6))

simplify183.0ms (1.3%)

Memory

37.7MiB live, 168.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	365	1614
1	1309	1593
2	4888	1583
0	9056	1467

Stop Event

1×	iter limit
1×	node limit

Counts

109 → 107

Calls

Call 1

Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(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)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -1 (* eps (sin x)))
(sin x)
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* 1/6 (* eps (sin x)))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 eps)
(* 1/24 eps)
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* eps (+ 1 (/ x eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))

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

rewrite200.0ms (1.5%)

Memory

-16.2MiB live, 178.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	200
0	60	200
1	218	200
2	1723	200
0	9909	200

Stop Event

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

Counts

21 → 186

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64))))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (sin.f64 x))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)))) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) #s(literal 2 binary64)))))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps)
(.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal -1/6 binary64) (.f64 (sin.f64 x) eps))))
(/.f64 (.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 3 binary64))) eps) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x))) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 2 binary64))))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)))) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal -1/6 binary64) (.f64 (sin.f64 x) eps))))
(/.f64 (.f64 eps (fma.f64 #s(literal 1/216 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x))) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) eps (.f64 (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) eps (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) eps))
(fma.f64 eps (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) (.f64 eps (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x))))
(+.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) eps) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) eps))
(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps)) eps) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x)) eps))
(+.f64 (.f64 eps (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x))) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))))
(+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) (.f64 eps (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (cos.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
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(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps))))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (neg.f64 eps)))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps))))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (neg.f64 eps)) (.f64 (neg.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))) (.f64 (neg.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (neg.f64 eps)))
(+.f64 (.f64 (neg.f64 eps) (sin.f64 x)) (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))))) (.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))))) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 x) (sin.f64 x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(fma.f64 (cos.f64 x) (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 x))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))))
(-.f64 (sin.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 x) (.f64 (neg.f64 (.f64 (cos.f64 x) eps)) #s(literal 1/2 binary64)))
(-.f64 (sin.f64 x) (.f64 (neg.f64 (cos.f64 x)) (.f64 #s(literal 1/2 binary64) eps)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))
(+.f64 (sin.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(*.f64 #s(literal 1/24 binary64) eps)
(*.f64 eps #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
(.f64 (.f64 #s(literal 1/6 binary64) eps) (sin.f64 x))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))
(.f64 (sin.f64 x) (.f64 #s(literal 1/6 binary64) eps))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))

eval55.0ms (0.4%)

Memory: 6.1MiB live, 50.5MiB allocated
Compiler: Compiled 9 606 to 1 317 computations (86.3% saved)

prune30.0ms (0.2%)

Memory

-18.7MiB live, 44.2MiB allocated

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	290	10	300
Fresh	0	2	2
Picked	1	4	5
Done	0	1	1
Total	291	17	308

Accuracy

100.0%

Counts

308 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	49.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
✓	99.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
▶	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
▶	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
▶	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 eps x) x) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
▶	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 724 to 504 computations (30.4% saved)

simplify160.0ms (1.2%)

Memory

39.0MiB live, 124.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	367
0	74	367
1	148	364
2	366	361
3	988	359
4	2475	359
5	4572	359
6	6144	359
0	8121	345

Stop Event

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

Calls

Call 1

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

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

localize293.0ms (2.2%)

Memory

-87.9MiB live, 306.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
accuracy	0.07847255168572895	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
accuracy	0.10546875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
accuracy	0.8774021739785078	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.00390625	(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
accuracy	0.0078125	(fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
accuracy	0.07847255168572895	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy	0.8625932181875111	#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0.0	(neg.f64 eps)
accuracy	0.07847255168572895	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
accuracy	0.10546875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
accuracy	0.8734959160793836	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.0	(*.f64 (neg.f64 x) eps)
accuracy	0.0	(neg.f64 x)
accuracy	0.8664994396042345	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	13.262510301317853	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0.0078125	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.015261291389095776	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
accuracy	0.015625	(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
accuracy	0.1015625	(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)

Samples

208.0ms	176×	2	valid
48.0ms	80×	1	valid

Compiler

Compiled 235 to 40 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

adjust: 67.0ms (34.2% of total)

ival-mult: 51.0ms (26% of total)

ival-cos: 47.0ms (24% of total)

ival-add: 18.0ms (9.2% of total)

const: 4.0ms (2% of total)

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

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

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

exact: 1.0ms (0.5% of total)

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

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

series20.0ms (0.1%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

22 → 81

Calls

Call 1

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

Calls

6 calls:

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

simplify166.0ms (1.2%)

Memory

-16.8MiB live, 71.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	287	1071
1	1026	1045
2	3675	997
0	8306	928

Stop Event

1×	iter limit
1×	node limit

Counts

81 → 80

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

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

rewrite204.0ms (1.5%)

Memory

14.3MiB live, 104.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	315
0	74	315
1	268	312
2	2061	312
0	9601	301

Stop Event

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

Counts

22 → 168

Calls

Call 1

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

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

eval27.0ms (0.2%)

Memory: 27.0MiB live, 27.0MiB allocated
Compiler: Compiled 8 888 to 1 095 computations (87.7% saved)

prune38.0ms (0.3%)

Memory

-29.3MiB live, 16.8MiB allocated

Pruning

18 alts after pruning (8 fresh and 10 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	2	5	7
Picked	0	5	5
Done	0	5	5
Total	239	18	257

Accuracy

100.0%

Counts

257 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	49.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
✓	99.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
▶	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
✓	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
✓	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
▶	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
▶	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (neg.f64 x) eps))))
✓	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 662 to 462 computations (30.2% saved)

simplify140.0ms (1%)

Memory

-2.1MiB live, 103.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	535
0	106	527
1	209	524
2	524	513
3	1604	511
4	3972	501
5	5610	501
0	8296	482

Stop Event

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

Calls

Call 1

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

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

localize580.0ms (4.3%)

Memory

2.4MiB live, 466.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.048378061523802154	(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
accuracy	0.057992109428145255	(cos.f64 (+.f64 x eps))
accuracy	0.7265448115444642	(PI.f64)
accuracy	31.492649169162206	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
accuracy	0.10546875	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
accuracy	0.26171875	(fma.f64 #s(literal -1/4 binary64) eps (*.f64 #s(literal -1/6 binary64) x))
accuracy	0.29296875	(*.f64 #s(literal -1/6 binary64) x)
accuracy	0.6046573109193738	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.0	(neg.f64 x)
accuracy	0.07847255168572895	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (neg.f64 x) eps))))
accuracy	0.12109375	(fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (neg.f64 x) eps))
accuracy	0.8625932181875111	#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (neg.f64 x) eps)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) eps)
accuracy	0.015261291389095776	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
accuracy	0.1015625	(.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy	58.49241957561333	#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.1015625	(.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps)
accuracy	0.10546875	(.f64 (.f64 eps eps) x)
accuracy	0.19140625	(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
accuracy	0.8782296032696157	#s(approx (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)))

Samples

431.0ms	174×	2	valid
84.0ms	79×	1	valid
9.0ms	3×	5	exit

Compiler

Compiled 329 to 65 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 472.0ms

ival-sin: 160.0ms (33.9% of total)

adjust: 110.0ms (23.3% of total)

ival-mult: 75.0ms (15.9% of total)

ival-cos: 61.0ms (12.9% of total)

ival-add: 29.0ms (6.1% of total)

const: 14.0ms (3% of total)

ival-sub: 13.0ms (2.8% of total)

ival-div: 5.0ms (1.1% of total)

ival-pi: 3.0ms (0.6% of total)

ival-neg: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series28.0ms (0.2%)

Memory

39.3MiB live, 39.3MiB allocated

Counts

27 → 158

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (+ (* (* eps eps) -1/2) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/4 eps) (* -1/6 x)) x) 1) x) (* 1/2 eps)) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x) (neg x) (* -1/6 x) (+ (* -1/4 eps) (* -1/6 x)) (PI))
4.0ms	eps	@	inf	((+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (+ (* (* eps eps) -1/2) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/4 eps) (* -1/6 x)) x) 1) x) (* 1/2 eps)) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x) (neg x) (* -1/6 x) (+ (* -1/4 eps) (* -1/6 x)) (PI))
4.0ms	eps	@	-inf	((+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (+ (* (* eps eps) -1/2) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/4 eps) (* -1/6 x)) x) 1) x) (* 1/2 eps)) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x) (neg x) (* -1/6 x) (+ (* -1/4 eps) (* -1/6 x)) (PI))
4.0ms	x	@	-inf	((+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (+ (* (* eps eps) -1/2) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/4 eps) (* -1/6 x)) x) 1) x) (* 1/2 eps)) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x) (neg x) (* -1/6 x) (+ (* -1/4 eps) (* -1/6 x)) (PI))
3.0ms	x	@	0	((+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) eps) (- (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (+ (* (* eps eps) -1/2) (* (neg x) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/4 eps) (* -1/6 x)) x) 1) x) (* 1/2 eps)) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (* (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) (* 1/24 (* eps eps)) (* (* eps eps) x) (neg x) (* -1/6 x) (+ (* -1/4 eps) (* -1/6 x)) (PI))

simplify151.0ms (1.1%)

Memory

-33.5MiB live, 107.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	474	2335
1	1660	2286
2	6243	2276
0	8439	2122

Stop Event

1×	iter limit
1×	node limit

Counts

158 → 156

Calls

Call 1

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

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

rewrite152.0ms (1.1%)

Memory

4.3MiB live, 91.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	469
0	106	461
1	442	458
2	3337	458
0	8157	436

Stop Event

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

Counts

27 → 305

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #s(literal 1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) x) #s(literal 2 binary64))) (-.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps) #s(literal 1/2 binary64)) eps) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) x)))
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(.f64 eps (.f64 #s(literal 1/24 binary64) eps))
(fabs.f64 (neg.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps)))
(fabs.f64 (.f64 (.f64 #s(literal 1/24 binary64) eps) eps))
(.f64 (.f64 x eps) eps)
(.f64 (neg.f64 eps) (.f64 (neg.f64 eps) x))
(.f64 (.f64 (neg.f64 x) eps) (neg.f64 eps))
(.f64 x (.f64 eps eps))
(.f64 (.f64 eps eps) x)
(.f64 eps (.f64 x eps))
(neg.f64 x)
(*.f64 #s(literal -1/6 binary64) x)
(*.f64 x #s(literal -1/6 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/16 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal -1/6 binary64) x) (*.f64 #s(literal -1/4 binary64) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64)) (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/4 binary64) eps) (*.f64 #s(literal 1/6 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/64 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) x) (-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))))))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)))
(/.f64 (fma.f64 #s(literal -1/64 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (.f64 (.f64 (*.f64 #s(literal -1/4 binary64) eps) #s(literal -1/6 binary64)) x))))
(/.f64 (fma.f64 #s(literal -1/64 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) x) (-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps)))))
(fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps))
(fma.f64 #s(literal -1/4 binary64) eps (*.f64 #s(literal -1/6 binary64) x))
(fma.f64 x #s(literal -1/6 binary64) (*.f64 #s(literal -1/4 binary64) eps))
(fma.f64 eps #s(literal -1/4 binary64) (*.f64 #s(literal -1/6 binary64) x))
(-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal 1/6 binary64) x))
(-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (neg.f64 eps) #s(literal -1/4 binary64)))
(-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal 1/4 binary64) eps))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) x) (-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))))) (/.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) x) (-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))))))
(+.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))
(+.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (PI.f64)))
(pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (neg.f64 (PI.f64)))
(fabs.f64 (PI.f64))
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))
(exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)

eval85.0ms (0.6%)

Memory: 16.4MiB live, 75.5MiB allocated
Compiler: Compiled 19 457 to 2 606 computations (86.6% saved)

prune22.0ms (0.2%)

Memory

-22.6MiB live, 25.0MiB allocated

Pruning

18 alts after pruning (5 fresh and 13 done)

	Pruned	Kept	Total
New	481	3	484
Fresh	1	2	3
Picked	2	3	5
Done	0	10	10
Total	484	18	502

Accuracy

100.0%

Counts

502 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	50.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	49.8%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
✓	99.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) #s(approx (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) (sin.f64 x)) eps))
	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (cos x) (+ (* eps (* 1/24 eps)) -1/2)) (* (* (sin x) eps) 1/6)) eps) #s(approx (+ (* (* (* eps eps) x) 1/6) (* (- (* 1/24 (* eps eps)) 1/2) eps)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) x))) (sin.f64 x)) eps))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
✓	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
✓	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
✓	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
✓	51.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
✓	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (neg.f64 x) eps))))
✓	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
✓	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 1 115 to 510 computations (54.3% saved)

regimes17.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory

-25.7MiB live, 19.5MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

-29.1MiB live, 15.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
3.0ms	x
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

8.7MiB live, 8.7MiB allocated

Accuracy

Total -17.6b remaining (-128.4%)

Threshold costs -17.6b (-128.4%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify90.0ms (0.7%)

Memory

-27.6MiB live, 27.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	87	242
1	167	242
2	381	240
3	1045	240
4	2368	238
5	3847	238
6	5091	238
7	6677	238

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations615.0ms (4.5%)

Memory

36.3MiB live, 229.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	296
1	308	293
2	779	293
3	2454	292
4	6244	292
0	8035	272
0	474	2335
1	1660	2286
2	6243	2276
0	8439	2122
0	365	1614
1	1309	1593
2	4888	1583
0	9056	1467

Stop Event

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

Compiler

Compiled 242 to 91 computations (62.4% saved)

preprocess51.0ms (0.4%)

Memory: -2.2MiB live, 43.5MiB allocated
Compiler: Compiled 532 to 224 computations (57.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze90.0ms (0.7%)

sample8.9s (65.8%)

explain226.0ms (1.7%)

preprocess23.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0%)

localize101.0ms (0.7%)

series4.0ms (0%)

simplify119.0ms (0.9%)

rewrite161.0ms (1.2%)

eval20.0ms (0.1%)

prune9.0ms (0.1%)

simplify179.0ms (1.3%)

localize281.0ms (2.1%)

series27.0ms (0.2%)

simplify183.0ms (1.3%)

rewrite200.0ms (1.5%)

eval55.0ms (0.4%)

prune30.0ms (0.2%)

simplify160.0ms (1.2%)

localize293.0ms (2.2%)

series20.0ms (0.1%)

simplify166.0ms (1.2%)

rewrite204.0ms (1.5%)

eval27.0ms (0.2%)

prune38.0ms (0.3%)

simplify140.0ms (1%)

localize580.0ms (4.3%)

series28.0ms (0.2%)

simplify151.0ms (1.1%)

rewrite152.0ms (1.1%)

eval85.0ms (0.6%)

prune22.0ms (0.2%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify90.0ms (0.7%)

derivations615.0ms (4.5%)

preprocess51.0ms (0.4%)

end0.0ms (0%)

Profiling