Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze49.0ms (0.4%)

Memory

5.9MiB live, 50.5MiB allocated; 18ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.2s (60.9%)

Memory

-149.3MiB live, 7 788.6MiB allocated; 2.5s collecting garbage

Samples

4.0s	25 651×	0	invalid
1.1s	5 129×	1	valid
315.0ms	3 127×	0	valid

Precisions

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

const: 1.1s (28.5% of total)

ival-sin: 871.0ms (22.5% of total)

ival-<: 312.0ms (8.1% of total)

ival-add: 300.0ms (7.8% of total)

ival-fabs: 257.0ms (6.7% of total)

ival-mult: 246.0ms (6.4% of total)

ival-sub: 241.0ms (6.2% of total)

adjust: 210.0ms (5.4% of total)

ival-<=: 176.0ms (4.6% of total)

ival-and: 97.0ms (2.5% of total)

exact: 41.0ms (1.1% of total)

ival-assert: 11.0ms (0.3% of total)

Bogosity

explain114.0ms (1%)

Memory

-8.1MiB live, 138.4MiB allocated; 16ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
238	1	(2.4185364921987094e-228 6.762651286286268e-231)	4	(-7.858801752117988e-290 1.293256148064356e-291)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	235	7

Confusion

	Predicted +	Predicted -
+	234	4
-	1	17

Precision

0.9957446808510638

Recall

0.9831932773109243

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	234	4	0
-	1	3	14

Precision?

0.9834710743801653

Recall?

1.0

Freqs

test

number	freq
0	21
1	235

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

52.0ms	318×	1	valid
9.0ms	194×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

adjust: 10.0ms (36.7% of total)

ival-sin: 10.0ms (36.7% of total)

ival-add: 4.0ms (14.7% of total)

ival-sub: 3.0ms (11% of total)

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

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

preprocess88.0ms (0.7%)

Memory

-8.0MiB live, 38.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	22	43
2	29	43
3	37	43
4	50	43
5	78	43
6	137	43
7	382	43
8	1447	43
9	5227	43
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	11	18
0	11	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.2%)

Memory

25.2MiB live, 25.2MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 (+.f64 x eps))
accuracy	0.0	(sin.f64 x)
accuracy	24.27391058339219	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

17.0ms	159×	1	valid
4.0ms	97×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

adjust: 5.0ms (37.2% of total)

ival-sin: 5.0ms (37.2% of total)

ival-sub: 2.0ms (14.9% of total)

ival-add: 2.0ms (14.9% of total)

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

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

series4.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Counts

4 → 34

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

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

simplify160.0ms (1.4%)

Memory

-2.4MiB live, 140.9MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	494
1	405	494
2	1292	487
3	4318	487
0	8199	458

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 34

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

rewrite186.0ms (1.6%)

Memory

-19.3MiB live, 168.7MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4478	16
0	8242	16

Stop Event

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

Counts

4 → 158

Calls

Call 1

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

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

eval44.0ms (0.4%)

Memory: -8.9MiB live, 35.8MiB allocated; 6ms collecting garbage
Compiler: Compiled 5 687 to 752 computations (86.8% saved)

prune5.0ms (0%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	181	5	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	181	6	187

Accuracy

100.0%

Counts

187 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 163 to 122 computations (25.2% saved)

simplify157.0ms (1.3%)

Memory

-9.2MiB live, 139.2MiB allocated; 12ms collecting garbage

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	202
0	59	192
1	108	192
2	266	189
3	864	189
4	4082	189
0	8192	189

Stop Event

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

Calls

Call 1

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

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

localize188.0ms (1.6%)

Memory

-2.0MiB live, 234.2MiB allocated; 17ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.010097509768442016	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
accuracy	0.14416754138909577	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.5782461283723842	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
accuracy	28.710272101045895	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.01171875	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.015625	(*.f64 (sin.f64 x) eps)
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.2069971778256539	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	0.9941732962535323	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	0.0	(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy	0.0078125	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Samples

157.0ms

256×

valid

Compiler

Compiled 179 to 36 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-cos: 45.0ms (34.9% of total)

adjust: 25.0ms (19.4% of total)

ival-mult: 25.0ms (19.4% of total)

ival-add: 13.0ms (10.1% of total)

ival-sin: 12.0ms (9.3% of total)

ival-sub: 5.0ms (3.9% of total)

ival-div: 3.0ms (2.3% of total)

exact: 1.0ms (0.8% of total)

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

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

series34.0ms (0.3%)

Memory

-2.4MiB live, 43.1MiB allocated; 4ms collecting garbage

Counts

20 → 118

Calls

Call 1

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

Outputs
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- eps (* -2 x))))))
#s(approx (+ 0 eps) #s(hole binary64 eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (cos (* -1 x)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x)))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1 x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
6.0ms	eps	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
5.0ms	x	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
4.0ms	x	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
4.0ms	x	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))

simplify169.0ms (1.4%)

Memory

32.3MiB live, 130.0MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	548	2514
1	1695	2409
2	6757	2390
0	8686	2229

Stop Event

1×	iter limit
1×	node limit

Counts

118 → 118

Calls

Call 1

Inputs
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- eps (* -2 x))))))
#s(approx (+ 0 eps) #s(hole binary64 eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (cos (* -1 x)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x)))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1 x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))

Outputs
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (/ (+ (* 2 x) eps) -2) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (fma.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x)) x)) x eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) (*.f64 x eps))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (* (sin x) eps) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) x) x (.f64 #s(literal -1/6 binary64) eps)) (.f64 x eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (sin.f64 eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps))))
#s(approx (* (sin eps) x) (*.f64 (sin.f64 eps) x))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* 2 x) eps) -2) (neg.f64 x))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (.f64 (*.f64 (sin.f64 eps) x) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (.f64 x x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) (.f64 x x)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (+ eps (* 2 x))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (/.f64 (sin.f64 eps) x)) (neg.f64 x))) (.f64 x x)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (neg.f64 x) (fma.f64 (sin.f64 eps) #s(literal 1/2 binary64) (/.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- eps (* -2 x))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (+ 0 eps) #s(hole binary64 eps))
#s(approx (+ 0 eps) eps)
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (cos (* -1 x)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) eps)
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) eps) eps) #s(literal 1/6 binary64)) eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 x eps) #s(literal 1/24 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/6 binary64))) eps) eps)) eps eps))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x)))
#s(approx (* (sin eps) x) (*.f64 x eps))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x))))))
#s(approx (* (sin eps) x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x) eps))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))))
#s(approx (* (sin eps) x) (.f64 (fma.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))) (.f64 eps eps) x) eps))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))))
#s(approx (* (sin eps) x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) eps) eps (.f64 #s(literal -1/6 binary64) x)) (*.f64 x eps)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1 x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))

rewrite84.0ms (0.7%)

Memory

11.2MiB live, 57.1MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	170
0	59	162
1	221	162
0	1996	162

Stop Event

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

Counts

20 → 194

Calls

Call 1

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

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

eval112.0ms (1%)

Memory: -37.3MiB live, 53.6MiB allocated; 10ms collecting garbage
Compiler: Compiled 9 179 to 1 354 computations (85.2% saved)

prune11.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	324	11	335
Fresh	0	0	0
Picked	3	2	5
Done	1	0	1
Total	328	13	341

Accuracy

100.0%

Counts

341 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	100.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))

Compiler

Compiled 592 to 408 computations (31.1% saved)

simplify166.0ms (1.4%)

Memory

-21.8MiB live, 77.0MiB allocated; 11ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
cost-diff	1	(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	1	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	435
0	86	429
1	164	429
2	543	426
3	2571	426
4	7196	426
0	8687	411

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 x eps))
eps
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/12 binary64) x) eps)
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

Outputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 x eps))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1/12 binary64) x) eps)
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize215.0ms (1.8%)

Memory

37.2MiB live, 227.7MiB allocated; 22ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
accuracy	0.11328125	(.f64 (.f64 #s(literal 1/12 binary64) x) eps)
accuracy	0.3671875	(*.f64 #s(literal 1/12 binary64) x)
accuracy	0.586274852126052	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy	0.01171875	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.2069971778256539	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.20703125	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	0.3741371054255876	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.010097509768442016	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
accuracy	0.1328125	(*.f64 eps (+.f64 x eps))
accuracy	0.5782461283723842	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
accuracy	0.9941732962535323	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.0078125	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Samples

98.0ms	159×	1	valid
55.0ms	96×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 267 to 53 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-mult: 54.0ms (45.6% of total)

adjust: 23.0ms (19.4% of total)

ival-add: 13.0ms (11% of total)

const: 9.0ms (7.6% of total)

ival-sin: 7.0ms (5.9% of total)

ival-sub: 4.0ms (3.4% of total)

ival-cos: 4.0ms (3.4% of total)

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

exact: 1.0ms (0.8% of total)

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

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

series31.0ms (0.3%)

Memory

5.4MiB live, 51.0MiB allocated; 5ms collecting garbage

Counts

24 → 114

Calls

Call 1

Inputs
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 eps eps)
(*.f64 eps (+.f64 x eps))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(*.f64 #s(literal 1/12 binary64) x)
(.f64 (.f64 #s(literal 1/12 binary64) x) eps)

Outputs
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* 1/12 x) #s(hole binary64 (* 1/12 x)))
#s(approx (* (* 1/12 x) eps) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps x)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1 x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (cos (* -1 x)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (/ (+ 0 eps) 2)) (* eps eps) (* eps (+ x eps)) (* 1/24 (* x x)) (* 1/12 x) (* (* 1/12 x) eps))
7.0ms	eps	@	0	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (/ (+ 0 eps) 2)) (* eps eps) (* eps (+ x eps)) (* 1/24 (* x x)) (* 1/12 x) (* (* 1/12 x) eps))
4.0ms	eps	@	inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (/ (+ 0 eps) 2)) (* eps eps) (* eps (+ x eps)) (* 1/24 (* x x)) (* 1/12 x) (* (* 1/12 x) eps))
4.0ms	x	@	-inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (/ (+ 0 eps) 2)) (* eps eps) (* eps (+ x eps)) (* 1/24 (* x x)) (* 1/12 x) (* (* 1/12 x) eps))
4.0ms	eps	@	-inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (/ (+ 0 eps) 2)) (* eps eps) (* eps (+ x eps)) (* 1/24 (* x x)) (* 1/12 x) (* (* 1/12 x) eps))

simplify144.0ms (1.2%)

Memory

-10.1MiB live, 178.1MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	493	2276
1	1476	2184
2	6209	2171
0	8374	2021

Stop Event

1×	iter limit
1×	node limit

Counts

114 → 114

Calls

Call 1

Inputs
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* 1/12 x) #s(hole binary64 (* 1/12 x)))
#s(approx (* (* 1/12 x) eps) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps x)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1 x))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (cos (* -1 x)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Outputs
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (/ (+ (* 2 x) eps) -2) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))))
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#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) eps)
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (fma.f64 (.f64 (+.f64 eps x) eps) (.f64 #s(literal -1/2 binary64) x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (* eps (+ x eps)) (*.f64 (+.f64 eps x) eps))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) (*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (* eps (+ x eps)) (.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) #s(hole binary64 (cos (* -1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (/ (+ (* 2 x) eps) -2) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) #s(hole binary64 (* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) (*.f64 eps eps)))
#s(approx (- (* (* 1/12 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
#s(approx (- (* (* 1/12 x) eps) 1/2) (*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))

rewrite142.0ms (1.2%)

Memory

-30.6MiB live, 94.4MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	353
0	86	347
1	320	347
0	3008	340

Stop Event

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

Counts

24 → 263

Calls

Call 1

Inputs
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 eps eps)
(*.f64 eps (+.f64 x eps))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(*.f64 #s(literal 1/12 binary64) x)
(.f64 (.f64 #s(literal 1/12 binary64) x) eps)

Outputs
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(-.f64 (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal -1 binary64)) (.f64 x #s(literal -1 binary64))) (.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64)))) (-.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal -1 binary64)) (.f64 x #s(literal -1 binary64)) (-.f64 (.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64))) (.f64 (.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64)))
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64)))
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(neg.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)))
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(fma.f64 (.f64 eps #s(literal 1/12 binary64)) x (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 (.f64 eps #s(literal 1/12 binary64)) x (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 (.f64 eps x) #s(literal 1/12 binary64) (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 (.f64 eps x) #s(literal 1/12 binary64) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64) (.f64 (*.f64 #s(literal 1/12 binary64) x) eps))
(fma.f64 (.f64 #s(literal 1/12 binary64) x) eps (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 (.f64 #s(literal 1/12 binary64) x) eps (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/12 binary64) (.f64 eps x) (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 #s(literal 1/12 binary64) (.f64 eps x) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x) (.f64 (*.f64 #s(literal 1/12 binary64) x) eps))
(fma.f64 eps (.f64 #s(literal 1/12 binary64) x) (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 eps (.f64 #s(literal 1/12 binary64) x) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 x (.f64 #s(literal 1/12 binary64) eps) (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 x (.f64 #s(literal 1/12 binary64) eps) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x)) (.f64 (.f64 #s(literal 1/12 binary64) x) eps))
(+.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)) (.f64 (.f64 #s(literal 1/12 binary64) x) eps))
(+.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) (.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x)))
(+.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) (.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))

eval76.0ms (0.6%)

Memory: 22.1MiB live, 68.9MiB allocated; 3ms collecting garbage
Compiler: Compiled 12 726 to 1 803 computations (85.8% saved)

prune60.0ms (0.5%)

Memory

-7.2MiB live, 39.4MiB allocated; 4ms collecting garbage

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	353	10	363
Fresh	2	4	6
Picked	4	1	5
Done	1	1	2
Total	360	16	376

Accuracy

100.0%

Counts

376 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	100.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))

Compiler

Compiled 837 to 553 computations (33.9% saved)

simplify234.0ms (2%)

Memory

3.8MiB live, 178.0MiB allocated; 41ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
cost-diff	2	(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
cost-diff	1	(fma.f64 x eps (*.f64 eps eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
cost-diff	0	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
cost-diff	1	(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	2	(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))
cost-diff	3	(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	489
0	94	469
1	185	465
2	696	461
3	3660	461
0	8043	450

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* eps (+ x eps)) (*.f64 eps x))
(*.f64 eps x)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(fma.f64 x eps (*.f64 eps eps))
eps
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(literal 1/24 binary64)
(.f64 (.f64 x x) eps)
(*.f64 x x)
x
eps
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps

Outputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) x)
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 x #s(literal 2 binary64) eps)
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (* eps (+ x eps)) (.f64 x eps)) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (* eps (+ x eps)) (.f64 x eps)) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
(fma.f64 #s(approx (* eps (+ x eps)) (.f64 x eps)) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* eps (+ x eps)) (*.f64 eps x))
#s(approx (* eps (+ x eps)) (*.f64 x eps))
(*.f64 eps x)
(*.f64 x eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
(fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(fma.f64 x eps (*.f64 eps eps))
(*.f64 (+.f64 x eps) eps)
eps
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
#s(literal 1/24 binary64)
(.f64 (.f64 x x) eps)
(*.f64 x x)
x
eps
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps

localize311.0ms (2.6%)

Memory

30.4MiB live, 457.3MiB allocated; 61ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.01171875	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.2069971778256539	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.25935244839430793	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
accuracy	0.07421875	(.f64 (.f64 x x) eps)
accuracy	0.2069971778256539	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
accuracy	0.3695756666541926	#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
accuracy	0.010097509768442016	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
accuracy	0.024969989932729534	(fma.f64 x eps (*.f64 eps eps))
accuracy	0.5782461283723842	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
accuracy	0.010097509768442016	(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
accuracy	0.01596665172363414	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
accuracy	0.5782461283723842	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
accuracy	12.798796190336349	#s(approx (* eps (+ x eps)) (*.f64 eps x))
accuracy	0.0	(PI.f64)
accuracy	0.0	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
accuracy	0.01953125	(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))

Samples

208.0ms	159×	1	valid
47.0ms	97×	0	valid

Compiler

Compiled 305 to 60 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 210.0ms

adjust: 54.0ms (25.7% of total)

ival-mult: 51.0ms (24.3% of total)

ival-sin: 33.0ms (15.7% of total)

ival-add: 28.0ms (13.3% of total)

ival-div: 18.0ms (8.6% of total)

const: 17.0ms (8.1% of total)

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

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

ival-sub: 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)

series71.0ms (0.6%)

Memory

-6.6MiB live, 85.1MiB allocated; 56ms collecting garbage

Counts

25 → 138

Calls

Call 1

Inputs
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))
(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
(fma.f64 x eps (*.f64 eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(PI.f64)
#s(approx (* eps (+ x eps)) (*.f64 eps x))
(.f64 (.f64 x x) eps)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))

Outputs
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 x))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ eps x)) (* 1/2 (/ (PI) x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* eps x)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps x)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* 1/2 eps) (* 1/2 (PI))) x)) 1)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI)))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/8 (* eps (sin (+ x (* 1/2 (PI)))))) (* 1/2 (cos (+ x (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/8 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* 2 (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI))))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/24 (* eps (cos (+ x (* 1/2 (PI)))))) (* 2 (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/24 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	0	((sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (/ (+ (* x 2) eps) 2) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (+ (* x eps) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (sin (/ (+ 0 eps) 2)) (PI) (* eps (+ x eps)) (* (* x x) eps) (+ (* -1/720 (* x x)) 1/24))
7.0ms	x	@	0	((sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (/ (+ (* x 2) eps) 2) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (+ (* x eps) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (sin (/ (+ 0 eps) 2)) (PI) (* eps (+ x eps)) (* (* x x) eps) (+ (* -1/720 (* x x)) 1/24))
5.0ms	eps	@	-inf	((sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (/ (+ (* x 2) eps) 2) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (+ (* x eps) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (sin (/ (+ 0 eps) 2)) (PI) (* eps (+ x eps)) (* (* x x) eps) (+ (* -1/720 (* x x)) 1/24))
5.0ms	x	@	inf	((sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (/ (+ (* x 2) eps) 2) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (+ (* x eps) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (sin (/ (+ 0 eps) 2)) (PI) (* eps (+ x eps)) (* (* x x) eps) (+ (* -1/720 (* x x)) 1/24))
5.0ms	eps	@	inf	((sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (/ (+ (* x 2) eps) 2) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (+ (* x eps) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (sin (/ (+ 0 eps) 2)) (PI) (* eps (+ x eps)) (* (* x x) eps) (+ (* -1/720 (* x x)) 1/24))

simplify671.0ms (5.7%)

Memory

-203.3MiB live, 165.7MiB allocated; 884ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	531	3100
1	1513	2964
2	6259	2941
0	8350	2719

Stop Event

1×	iter limit
1×	node limit

Counts

138 → 138

Calls

Call 1

Inputs
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (pow eps 2)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 x))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ eps x)) (* 1/2 (/ (PI) x)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* eps x)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps x)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* 1/2 eps) (* 1/2 (PI))) x)) 1)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI)))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/8 (* eps (sin (+ x (* 1/2 (PI)))))) (* 1/2 (cos (+ x (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/8 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* 2 (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI))))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/24 (* eps (cos (+ x (* 1/2 (PI)))))) (* 2 (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/24 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))))

Outputs
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (sin.f64 (*.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (fma.f64 (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) x (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (fma.f64 (fma.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) eps))) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) x (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) x (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* x 2) eps) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (/ (+ (* x 2) eps) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (*.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x (sin.f64 (*.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x)) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x (sin.f64 (*.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
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#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
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#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
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#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (sin.f64 (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x)))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (/ (+ (* x 2) eps) 2) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* 1/2 eps) (* 1/2 (PI))) x)) 1)))))
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#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x)) (neg.f64 x))) (*.f64 x x)))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* eps (+ x eps)) (*.f64 (fma.f64 eps (/.f64 eps x) eps) x))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x)) (neg.f64 x))) (*.f64 x x)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* eps (+ x eps)) (*.f64 (fma.f64 eps (/.f64 eps x) eps) x))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI)))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/8 (* eps (sin (+ x (* 1/2 (PI)))))) (* 1/2 (cos (+ x (* 1/2 (PI))))))))))
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#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/8 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (.f64 #s(literal -1/8 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) eps (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal 1/2 binary64))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
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#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* 2 (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI))))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/6 binary64)) eps (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal 1/2 binary64))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/24 (* eps (cos (+ x (* 1/2 (PI)))))) (* 2 (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/6 binary64))) eps (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal 1/2 binary64))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 eps x) eps) eps))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (* eps (+ x eps)) (*.f64 (+.f64 eps x) eps))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 eps x) eps) eps))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/24 (pow x 2)) 1/2))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (sin (/ (+ 0 eps) 2)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (* eps (+ x eps)) (*.f64 (+.f64 eps x) eps))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (/ (+ (* x 2) eps) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))
#s(approx (+ (* x eps) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (* eps (+ x eps)) (.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))
#s(approx (sin (/ (+ 0 eps) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* eps (+ x eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (* eps (+ x eps)) (.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (sin.f64 (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x)))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (/ (+ (* x 2) eps) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) (*.f64 eps eps)))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ (* (* -1/2 x) (+ (* x eps) (* eps eps))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) (*.f64 eps eps)))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))))
#s(approx (+ (* (+ (* 1/24 (* (* x x) eps)) (* -1/2 eps)) (* x x)) eps) (.f64 (neg.f64 eps) (fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))))

rewrite141.0ms (1.2%)

Memory

-5.6MiB live, 188.9MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	398
0	94	380
1	410	376
0	3977	368

Stop Event

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

Counts

25 → 357

Calls

Call 1

Inputs
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))
(+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
(fma.f64 x eps (*.f64 eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(PI.f64)
#s(approx (* eps (+ x eps)) (*.f64 eps x))
(.f64 (.f64 x x) eps)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))

Outputs
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64))) (.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) (-.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) (.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64) (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)))
(sin.f64 (/.f64 (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64)))
(-.f64 (.f64 (cos.f64 (.f64 x #s(literal 1 binary64))) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal 1 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(-.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 (neg.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(cos.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64)))) (-.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 eps #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 eps #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (-.f64 (.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) (.f64 (.f64 x #s(literal 1 binary64)) (/.f64 eps #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 2 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (neg.f64 eps))) #s(literal -4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) eps)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 #s(literal 2 binary64) x)))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64)))
(neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64)))
(fma.f64 x #s(literal 1 binary64) (/.f64 eps #s(literal 2 binary64)))
(+.f64 (fma.f64 x #s(literal 1 binary64) #s(literal 0 binary64)) (/.f64 eps #s(literal 2 binary64)))
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(+.f64 (/.f64 eps #s(literal 2 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 eps #s(literal 2 binary64)))
(/.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(/.f64 (+.f64 (neg.f64 (PI.f64)) (neg.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal -2 binary64))
(/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (neg.f64 (PI.f64))) #s(literal -2 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (PI.f64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps))) #s(literal -2 binary64))
(/.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal -4 binary64))
(/.f64 (fma.f64 (neg.f64 (PI.f64)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (PI.f64)) #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(literal -4 binary64))
(/.f64 (fma.f64 (PI.f64) #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)))) #s(literal -4 binary64))
(/.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (PI.f64))) #s(literal -4 binary64))
(/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (PI.f64)))) #s(literal -4 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (PI.f64)) #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (PI.f64)) #s(literal 4 binary64)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 4 binary64))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)) (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 x #s(literal 1 binary64) (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (PI.f64)) #s(literal 2 binary64))) (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (PI.f64)) #s(literal 2 binary64))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 x #s(literal 1 binary64))) (/.f64 eps #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(+.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 4 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
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eval60.0ms (0.5%)

Memory: 17.8MiB live, 109.2MiB allocated; 8ms collecting garbage
Compiler: Compiled 17 564 to 2 242 computations (87.2% saved)

prune23.0ms (0.2%)

Memory

-7.1MiB live, 43.5MiB allocated; 6ms collecting garbage

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	462	4	466
Fresh	3	6	9
Picked	3	2	5
Done	0	2	2
Total	468	14	482

Accuracy

100.0%

Counts

482 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))))
	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	100.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))

Compiler

Compiled 1 188 to 458 computations (61.4% saved)

regimes28.0ms (0.2%)

Memory

-10.6MiB live, 33.7MiB allocated; 7ms collecting garbage

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))

Outputs

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

Calls

3 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.2%)

Memory

26.7MiB live, 26.7MiB allocated; 0ms collecting garbage

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-15.2MiB live, 29.9MiB allocated; 5ms collecting garbage

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

35.3MiB live, 35.3MiB allocated; 0ms collecting garbage

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))

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

Calls

3 calls:

5.0ms	eps
5.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.2%)

Memory

-5.4MiB live, 40.8MiB allocated; 2ms collecting garbage

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes42.0ms (0.4%)

Memory

-12.8MiB live, 39.1MiB allocated; 33ms collecting garbage

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

31.0ms	eps
5.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 eps x) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x eps (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps))))

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

-38.1MiB live, 10.5MiB allocated; 5ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.1%	1	`x`
99.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify51.0ms (0.4%)

Memory

-11.4MiB live, 34.7MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	253
1	134	253
2	290	251
3	1029	251
4	5287	251

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

Outputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (fma.f64 (+.f64 (PI.f64) eps) #s(literal 1/2 binary64) x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) eps) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

derivations546.0ms (4.6%)

Memory

9.3MiB live, 281.0MiB allocated; 33ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 261 to 94 computations (64% saved)

preprocess55.0ms (0.5%)

Memory: 31.9MiB live, 76.2MiB allocated; 8ms collecting garbage
Compiler: Compiled 566 to 226 computations (60.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze49.0ms (0.4%)

sample7.2s (60.9%)

explain114.0ms (1%)

preprocess88.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize28.0ms (0.2%)

series4.0ms (0%)

simplify160.0ms (1.4%)

rewrite186.0ms (1.6%)

eval44.0ms (0.4%)

prune5.0ms (0%)

simplify157.0ms (1.3%)

localize188.0ms (1.6%)

series34.0ms (0.3%)

simplify169.0ms (1.4%)

rewrite84.0ms (0.7%)

eval112.0ms (1%)

prune11.0ms (0.1%)

simplify166.0ms (1.4%)

localize215.0ms (1.8%)

series31.0ms (0.3%)

simplify144.0ms (1.2%)

rewrite142.0ms (1.2%)

eval76.0ms (0.6%)

prune60.0ms (0.5%)

simplify234.0ms (2%)

localize311.0ms (2.6%)

series71.0ms (0.6%)

simplify671.0ms (5.7%)

rewrite141.0ms (1.2%)

eval60.0ms (0.5%)

prune23.0ms (0.2%)

regimes28.0ms (0.2%)

regimes18.0ms (0.2%)

regimes21.0ms (0.2%)

regimes17.0ms (0.1%)

regimes18.0ms (0.2%)

regimes42.0ms (0.4%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify51.0ms (0.4%)

derivations546.0ms (4.6%)

preprocess55.0ms (0.5%)

end0.0ms (0%)

Profiling