Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze47.0ms (0.4%)

Memory

17.2MiB live, 60.3MiB allocated; 13ms 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)

sample7.6s (57.7%)

Memory

-167.7MiB live, 8 611.6MiB allocated; 2.4s collecting garbage

Samples

4.3s	26 173×	0	invalid
1.1s	5 167×	1	valid
401.0ms	3 089×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.7s

ival-sin: 771.0ms (21% of total)

const: 735.0ms (20% of total)

ival-add: 373.0ms (10.2% of total)

ival-fabs: 305.0ms (8.3% of total)

ival-mult: 303.0ms (8.3% of total)

ival-<=: 296.0ms (8.1% of total)

ival-<: 249.0ms (6.8% of total)

adjust: 240.0ms (6.5% of total)

ival-sub: 229.0ms (6.2% of total)

ival-and: 107.0ms (2.9% of total)

exact: 49.0ms (1.3% of total)

ival-assert: 15.0ms (0.4% of total)

Bogosity

explain97.0ms (0.7%)

Memory

-10.0MiB live, 81.9MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
218	2	(1.781589509096575e-274 1.4196471894782958e-277)	2	(-1.2240955723698952e-28 2.4517030511719255e-30)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
4	0	-	1	(-22.032762950454796 0.0016469131109583413)	`(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	218	8
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	3	0

Confusion

	Predicted +	Predicted -
+	217	3
-	2	34

Precision

0.9908675799086758

Recall

0.9863636363636363

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	217	2	1
-	2	5	29

Precision?

0.9690265486725663

Recall?

0.9954545454545455

Freqs

test

number	freq
0	37
1	217
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms	306×	1	valid
11.0ms	206×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sin: 11.0ms (37.9% of total)

adjust: 9.0ms (31% of total)

ival-add: 4.0ms (13.8% of total)

ival-sub: 4.0ms (13.8% of total)

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

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

preprocess47.0ms (0.4%)

Memory

-18.8MiB live, 26.9MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	22	43
2	29	43
3	37	43
4	49	43
5	71	43
6	93	43
7	147	43
8	231	43
9	385	43
10	1010	43
11	4371	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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

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

23.6MiB live, 23.6MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.15103818766683366	(sin.f64 (+.f64 x eps))
accuracy	23.96239090386602	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

17.0ms	153×	1	valid
5.0ms	103×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

adjust: 5.0ms (35% of total)

ival-sin: 5.0ms (35% of total)

ival-add: 2.0ms (14% of total)

ival-sub: 2.0ms (14% of total)

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

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

series4.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Counts

4 → 31

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

simplify143.0ms (1.1%)

Memory

-3.3MiB live, 91.5MiB allocated; 15ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

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

rewrite162.0ms (1.2%)

Memory

22.1MiB live, 111.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Counts

4 → 154

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)))
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(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (*.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)

eval73.0ms (0.6%)

Memory: -54.8MiB live, 38.4MiB allocated; 54ms collecting garbage
Compiler: Compiled 5 510 to 734 computations (86.7% saved)

prune10.0ms (0.1%)

Memory

-34.7MiB live, 13.6MiB allocated; 4ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	167	10	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	167	11	178

Accuracy

99.9%

Counts

178 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.5%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
	34.5%	(/.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)))))
	34.5%	(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
	62.6%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
✓	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.8%	(.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))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
▶	99.5%	#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))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 371 to 260 computations (29.9% saved)

simplify109.0ms (0.8%)

Memory

33.2MiB live, 77.7MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	0	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
cost-diff	0	(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)))
cost-diff	0	(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))
cost-diff	0	(.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)
cost-diff	0	#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))
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	(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: 3 (0.0ms)

Iter	Nodes	Cost
0	40	268
0	71	258
1	140	258
2	393	258
3	1539	255
4	4823	255
5	7283	255
0	8025	255

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

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

localize187.0ms (1.4%)

Memory

-15.7MiB live, 167.8MiB allocated; 27ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 eps)
accuracy	0.015625	(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
accuracy	0.0234375	(*.f64 (sin.f64 eps) (cos.f64 x))
accuracy	23.98648136135176	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
accuracy	0.0234375	(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)))
accuracy	0.02734375	(.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)
accuracy	0.30868131178350094	#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))
accuracy	0.3359375	(.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))
accuracy	0.01171875	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy	0.015625	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.01953125	(*.f64 (sin.f64 x) eps)
accuracy	0.8335320776648085	#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	(sin.f64 eps)
accuracy	2.454145821974216	#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	0.01953125	(.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))))
accuracy	0.1161471173439094	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

104.0ms	160×	1	valid
31.0ms	93×	0	valid
6.0ms	2×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 250 to 44 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 114.0ms

adjust: 31.0ms (27.2% of total)

ival-mult: 30.0ms (26.3% of total)

ival-add: 18.0ms (15.8% of total)

ival-sin: 13.0ms (11.4% of total)

ival-cos: 8.0ms (7% of total)

const: 7.0ms (6.1% of total)

ival-sub: 4.0ms (3.5% of total)

ival-div: 3.0ms (2.6% of total)

exact: 1.0ms (0.9% of total)

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

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

series34.0ms (0.3%)

Memory

36.3MiB live, 36.3MiB allocated; 0ms collecting garbage

Counts

22 → 137

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

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1/6 (* eps (cos x)))
(* (cos x) (sin eps))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	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)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (* (cos x) eps) -1/6) (* (sin eps) (cos x)))
6.0ms	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)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (* (cos x) eps) -1/6) (* (sin eps) (cos x)))
5.0ms	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)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (* (cos x) eps) -1/6) (* (sin eps) (cos x)))
4.0ms	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)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (* (cos x) eps) -1/6) (* (sin eps) (cos x)))
4.0ms	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)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (* (cos x) eps) -1/6) (* (sin eps) (cos x)))

simplify177.0ms (1.3%)

Memory

-5.1MiB live, 128.8MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	495	2059
1	1859	1970
2	7019	1956
0	8345	1788

Stop Event

1×	iter limit
1×	node limit

Counts

137 → 135

Calls

Call 1

Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1/6 (* eps (cos x)))
(* (cos x) (sin eps))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.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))
(+ (* 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)))))))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.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)))
(+ (* 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))))))))))
(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 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(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))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(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))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(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)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.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)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 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))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/6 binary64) eps) eps) x) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64))) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/12 binary64) eps)) x (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(+ (sin eps) (* -1 x))
(-.f64 (sin.f64 eps) x)
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(fma.f64 (-.f64 (.f64 (.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)) x (sin.f64 eps))
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(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)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(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)))
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/12 binary64) (*.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/12 binary64) eps)) x) x (*.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/144 binary64) eps)) x) x (.f64 #s(literal 1/12 binary64) eps)) (.f64 x x) (*.f64 #s(literal -1/6 binary64) eps))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(fma.f64 (.f64 (sin.f64 eps) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 eps) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (sin.f64 eps) (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.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)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
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(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (sin.f64 x))) eps (cos.f64 x))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (sin.f64 x)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
(sin x)
(sin.f64 x)
(- (* (cos x) (sin eps)) (sin x))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/6 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))
(* (cos x) (sin eps))
(*.f64 (cos.f64 x) (sin.f64 eps))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.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)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(* 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)))))))))))
(.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)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(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)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
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(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(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)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(cos x)
(cos.f64 x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
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(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
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(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* eps (cos x)) (sin x))
(-.f64 (*.f64 (cos.f64 x) eps) (sin.f64 x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(-.f64 (.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x)) eps) (sin.f64 x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(-.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))) (*.f64 (cos.f64 x) eps)) (sin.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(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))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.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)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
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(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x)) eps)
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))) (*.f64 (cos.f64 x) eps))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
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(* eps (- (* -1 (/ x eps)) 1/2))
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(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* 1/24 (* (pow eps 4) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)) (sin.f64 x))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 4 binary64)))
(* 1/24 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 3 binary64)))
(* 1/24 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/24 binary64))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)) (*.f64 eps eps))
(cos eps)
(cos.f64 eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.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)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/24 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (neg.f64 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) (neg.f64 eps))) eps) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite225.0ms (1.7%)

Memory

-24.8MiB live, 170.5MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	218
0	71	204
1	281	204
2	2538	204
0	8507	204

Stop Event

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

Counts

22 → 416

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

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

eval75.0ms (0.6%)

Memory: 51.2MiB live, 139.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 19 149 to 2 458 computations (87.2% saved)

prune35.0ms (0.3%)

Memory

-67.4MiB live, 49.2MiB allocated; 17ms collecting garbage

Pruning

27 alts after pruning (24 fresh and 3 done)

	Pruned	Kept	Total
New	548	21	569
Fresh	2	3	5
Picked	3	2	5
Done	0	1	1
Total	553	27	580

Accuracy

100.0%

Counts

580 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.3%	(fma.f64 (sin.f64 x) #s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
	62.6%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
✓	62.3%	(-.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)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
▶	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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)))))
	99.8%	(.f64 (.f64 #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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.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))))
▶	98.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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))))
	51.8%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.5%	#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))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.0%	#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))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
▶	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	6.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
▶	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
	97.4%	#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)))
	96.1%	#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 eps) eps)))
	99.8%	#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))))

Compiler

Compiled 1 476 to 1 010 computations (31.6% saved)

simplify153.0ms (1.2%)

Memory

6.4MiB live, 191.9MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
cost-diff	1	(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
cost-diff	2	(+.f64 #s(literal 0 binary64) eps)
cost-diff	3	(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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	0	(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
cost-diff	1	(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
cost-diff	1	(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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)) #s(literal 1 binary64)) eps))
cost-diff	1	(*.f64 x #s(literal -1 binary64))
cost-diff	1	(cos.f64 (*.f64 x #s(literal -1 binary64)))
cost-diff	1	(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
cost-diff	2	(+.f64 #s(literal 0 binary64) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	565
0	120	536
1	229	520
2	663	513
3	2602	511
4	6640	511
0	8166	484

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)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 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)
(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
(.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64))))
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))
(sin.f64 (/.f64 eps #s(literal -2 binary64)))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
x
(.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
#s(literal 1/24 binary64)
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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 (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)
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (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)
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
x
(PI.f64)

Outputs
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
(.f64 (fma.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal -2 binary64))) (.f64 (cos.f64 x) (cos.f64 (/.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)
(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
(fma.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal -2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))))
(.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64))))
(*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(cos.f64 (/.f64 eps #s(literal 2 binary64)))
(/.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(cos.f64 x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
#s(literal -1 binary64)
(.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))
(*.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(sin.f64 (/.f64 eps #s(literal -2 binary64)))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
(neg.f64 (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
x
(.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 (.f64 #s(literal 1/24 binary64) eps) eps)
#s(literal 1/24 binary64)
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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)))
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x))
(/.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)
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) (.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)
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) x)
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64)))
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
x
(PI.f64)

localize266.0ms (2%)

Memory

15.3MiB live, 299.8MiB allocated; 23ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(PI.f64)
accuracy	0.01953125	(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
accuracy	0.10803097933514606	(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.01953125	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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))))
accuracy	0.1161471173439094	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.7652533142052622	#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.1953125	(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
accuracy	0.30868131178350094	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
accuracy	0.34765625	(*.f64 #s(literal -1/6 binary64) eps)
accuracy	1.5932243507042052	#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
accuracy	0.015625	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.8335320776648085	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
accuracy	2.476243687199012	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
accuracy	0.01171875	(.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64))))
accuracy	0.015625	(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
accuracy	0.01953125	(.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))

Samples

160.0ms	153×	1	valid
54.0ms	103×	0	valid

Compiler

Compiled 446 to 73 computations (83.6% saved)

Precisions

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

ival-mult: 51.0ms (28.9% of total)

ival-sin: 36.0ms (20.4% of total)

adjust: 32.0ms (18.1% of total)

ival-add: 20.0ms (11.3% of total)

ival-cos: 11.0ms (6.2% of total)

const: 10.0ms (5.7% of total)

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

ival-sub: 6.0ms (3.4% of total)

ival-pi: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series42.0ms (0.3%)

Memory

-12.3MiB live, 38.8MiB allocated; 8ms collecting garbage

Counts

28 → 158

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
(.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64))))
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(PI.f64)

Outputs
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* -1 (* x (sin (* -1/2 eps))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* 1/6 (* (pow x 2) (sin (* -1/2 eps))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/6 (sin (* -1/2 eps)))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
(+ (cos (* -1/2 eps)) (* -1/2 (* (pow x 2) (cos (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* 1/24 (* (pow x 2) (cos (* -1/2 eps)))))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* -1/2 eps)))) (* 1/24 (cos (* -1/2 eps))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))
(cos (* -1 x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(* 1/2 (- (PI) (* 2 x)))
(+ (* -1/2 eps) (* 1/2 (- (PI) (* 2 x))))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* -1/2 (* eps (sin (* -1 x))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* 1/48 (* (pow eps 2) (sin (* -1 x))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin (* -1 x)))) (* 1/48 (sin (* -1 x)))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* 1/48 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (sin (* -1 x))) (* 1/645120 (* (pow eps 2) (sin (* -1 x))))))))))
(+ (cos (* -1 x)) (* -1/8 (* (pow eps 2) (cos (* -1 x)))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* 1/384 (* (pow eps 2) (cos (* -1 x)))))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos (* -1 x)))) (* 1/384 (cos (* -1 x))))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/6 eps)
(* 1/24 (pow eps 2))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	-inf	((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* eps eps)) 1/2) (- (* 1/24 (* eps eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (/ eps -2)) (sin (* x -1))) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (cos (/ eps -2)) (cos (* x -1))) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (* 1/24 (* eps eps)) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
10.0ms	x	@	inf	((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* eps eps)) 1/2) (- (* 1/24 (* eps eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (/ eps -2)) (sin (* x -1))) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (cos (/ eps -2)) (cos (* x -1))) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (* 1/24 (* eps eps)) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
6.0ms	eps	@	inf	((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* eps eps)) 1/2) (- (* 1/24 (* eps eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (/ eps -2)) (sin (* x -1))) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (cos (/ eps -2)) (cos (* x -1))) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (* 1/24 (* eps eps)) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
6.0ms	x	@	-inf	((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* eps eps)) 1/2) (- (* 1/24 (* eps eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (/ eps -2)) (sin (* x -1))) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (cos (/ eps -2)) (cos (* x -1))) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (* 1/24 (* eps eps)) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
4.0ms	eps	@	0	((+ 0 eps) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1)))) (cos (* x -1)) (* x -1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (* 1/12 (* eps eps)) 1/2) (- (* 1/24 (* eps eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (/ eps -2)) (sin (* x -1))) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (cos (/ eps -2)) (cos (* x -1))) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (* 1/24 (* eps eps)) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))

simplify176.0ms (1.3%)

Memory

37.8MiB live, 127.1MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	585	2543
1	2187	2411
0	8393	2213

Stop Event

1×	iter limit
1×	node limit

Counts

158 → 157

Calls

Call 1

Inputs
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* -1 (* x (sin (* -1/2 eps))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* 1/6 (* (pow x 2) (sin (* -1/2 eps))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/6 (sin (* -1/2 eps)))))))
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
(+ (cos (* -1/2 eps)) (* -1/2 (* (pow x 2) (cos (* -1/2 eps)))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* 1/24 (* (pow x 2) (cos (* -1/2 eps)))))))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* -1/2 eps)))) (* 1/24 (cos (* -1/2 eps))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))
(cos (* -1 x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(* 1/2 (- (PI) (* 2 x)))
(+ (* -1/2 eps) (* 1/2 (- (PI) (* 2 x))))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* -1/2 (* eps (sin (* -1 x))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* 1/48 (* (pow eps 2) (sin (* -1 x))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin (* -1 x)))) (* 1/48 (sin (* -1 x)))))))
(* eps (+ (* -1/2 (sin (* -1 x))) (* (pow eps 2) (+ (* 1/48 (sin (* -1 x))) (* (pow eps 2) (+ (* -1/3840 (sin (* -1 x))) (* 1/645120 (* (pow eps 2) (sin (* -1 x))))))))))
(+ (cos (* -1 x)) (* -1/8 (* (pow eps 2) (cos (* -1 x)))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* 1/384 (* (pow eps 2) (cos (* -1 x)))))))
(+ (cos (* -1 x)) (* (pow eps 2) (+ (* -1/8 (cos (* -1 x))) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos (* -1 x)))) (* 1/384 (cos (* -1 x))))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/6 eps)
(* 1/24 (pow eps 2))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))

Outputs
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(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)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(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)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.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))
(* -1 x)
(neg.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(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))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #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))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x)) x)) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 #s(literal 2 binary64) (.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)))))
(+ (* 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)))))))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal 2 binary64) (.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))))))
(+ (* 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))))))))))
(fma.f64 #s(literal 2 binary64) (.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)))) (.f64 (.f64 (fma.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.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)))) x) x))
(sin (* 1/2 (- (PI) eps)))
(sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(fma.f64 (neg.f64 x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) x) (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(* 1/2 (- (PI) eps))
(*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (neg.f64 x))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(.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)))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (.f64 (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (.f64 (.f64 (neg.f64 x) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (.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))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(fma.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)) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (.f64 (fma.f64 (neg.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x)) x))
(* -1 (* x (sin (* -1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x)
(* x (+ (* -1 (sin (* -1/2 eps))) (* 1/6 (* (pow x 2) (sin (* -1/2 eps))))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/6 (sin (* -1/2 eps)))))))
(.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) x)
(* x (+ (* -1 (sin (* -1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* -1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* -1/2 eps))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))) (.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) x)
(+ (cos (* -1/2 eps)) (* -1/2 (* (pow x 2) (cos (* -1/2 eps)))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* 1/24 (* (pow x 2) (cos (* -1/2 eps)))))))
(fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* -1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* -1/2 eps)))) (* 1/24 (cos (* -1/2 eps))))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
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(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 4 binary64)))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(.f64 (-.f64 (.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) eps)
(* 1/24 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(.f64 (neg.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/24 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (neg.f64 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))) (neg.f64 eps))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps)))

rewrite229.0ms (1.7%)

Memory

-10.9MiB live, 178.2MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	405
0	120	366
1	473	357
2	3876	357
0	8221	345

Stop Event

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

Counts

28 → 477

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
(.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64))))
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(PI.f64)

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

eval116.0ms (0.9%)

Memory: -5.7MiB live, 138.3MiB allocated; 16ms collecting garbage
Compiler: Compiled 20 720 to 2 783 computations (86.6% saved)

prune68.0ms (0.5%)

Memory

6.7MiB live, 96.5MiB allocated; 7ms collecting garbage

Pruning

34 alts after pruning (29 fresh and 5 done)

	Pruned	Kept	Total
New	519	13	532
Fresh	3	16	19
Picked	3	2	5
Done	0	3	3
Total	525	34	559

Accuracy

100.0%

Counts

559 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.3%	(fma.f64 (sin.f64 x) #s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
	62.6%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
✓	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) #s(approx (* (sin (/ eps -2)) (sin (* x -1))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64))) eps))))
	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (+.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	99.8%	(.f64 (.f64 #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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.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))))
	98.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
▶	98.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
▶	51.8%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
▶	50.6%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.5%	#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))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.0%	#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))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	47.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	6.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
✓	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
	97.4%	#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)))
▶	96.1%	#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 eps) eps)))
▶	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	97.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
	99.8%	#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))))

Compiler

Compiled 2 172 to 1 490 computations (31.4% saved)

simplify108.0ms (0.8%)

Memory

-8.7MiB live, 90.8MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
cost-diff	6	(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
cost-diff	1	(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
cost-diff	1	(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
cost-diff	6	(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 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 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 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 eps) eps)))
cost-diff	0	(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
cost-diff	0	(.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	687
0	136	677
1	285	672
2	923	653
3	4152	645
0	8041	617

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(literal 2 binary64)
(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 x)
x
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 x)
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 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 eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps))
(.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
x
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(neg.f64 eps)
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
#s(literal -1/2 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
(cos.f64 x)
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
(neg.f64 eps)

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.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)) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(sin.f64 x)
x
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(cos.f64 x)
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps)
(.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (*.f64 (neg.f64 eps) eps))
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
eps
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
#s(literal 1/12 binary64)
x
(fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(neg.f64 eps)
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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 (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 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 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 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)) (neg.f64 (*.f64 eps eps)))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (neg.f64 eps) eps))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
(cos.f64 x)
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
(neg.f64 eps)

localize323.0ms (2.5%)

Memory

12.0MiB live, 395.9MiB allocated; 48ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))
accuracy	0.01953125	(*.f64 (sin.f64 x) eps)
accuracy	0.8335320776648085	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
accuracy	30.05363687367328	(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
accuracy	0.0	#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.01953125	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
accuracy	0.1161471173439094	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.7652533142052622	#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.30868131178350094	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
accuracy	0.34765625	(*.f64 #s(literal -1/6 binary64) eps)
accuracy	1.5932243507042052	#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
accuracy	30.05363687367328	(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps))
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.8335320776648085	#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 eps) eps)))
accuracy	2.4821573048374663	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps))
accuracy	0.0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.01171875	(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.01171875	(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.01953125	(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))

Samples

189.0ms	153×	1	valid
60.0ms	103×	0	valid

Compiler

Compiled 471 to 86 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 211.0ms

ival-mult: 79.0ms (37.5% of total)

adjust: 39.0ms (18.5% of total)

ival-add: 30.0ms (14.2% of total)

ival-cos: 17.0ms (8.1% of total)

ival-sin: 15.0ms (7.1% of total)

ival-div: 10.0ms (4.7% of total)

const: 10.0ms (4.7% of total)

ival-sub: 6.0ms (2.8% of total)

ival-neg: 2.0ms (0.9% of total)

exact: 1.0ms (0.5% of total)

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

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

series38.0ms (0.3%)

Memory

14.0MiB live, 59.6MiB allocated; 4ms collecting garbage

Counts

27 → 151

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 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 eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 eps eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (sin.f64 x) eps)

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1/2 x)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))))
(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
(+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (cos x) (cos (* 1/2 eps)))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(cos (+ x (* 1/2 eps)))
(cos (* -1/2 (+ eps (* 2 x))))
(* eps (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (* eps x))))
-1/2
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/12 (pow eps 2)) 1/2)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(pow eps 2)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/6 eps)
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(cos (- x (* -1/2 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x))) (neg eps)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/2 eps) (/ (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (+ (* -1/2 (* (sin x) eps)) (cos x)) (* (cos x) (cos (* 1/2 eps))) (* eps eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* (sin x) eps))
7.0ms	x	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x))) (neg eps)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/2 eps) (/ (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (+ (* -1/2 (* (sin x) eps)) (cos x)) (* (cos x) (cos (* 1/2 eps))) (* eps eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* (sin x) eps))
6.0ms	eps	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x))) (neg eps)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/2 eps) (/ (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (+ (* -1/2 (* (sin x) eps)) (cos x)) (* (cos x) (cos (* 1/2 eps))) (* eps eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* (sin x) eps))
6.0ms	eps	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x))) (neg eps)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/2 eps) (/ (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (+ (* -1/2 (* (sin x) eps)) (cos x)) (* (cos x) (cos (* 1/2 eps))) (* eps eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* (sin x) eps))
4.0ms	eps	@	0	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (* (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin x) (sin (* -1/2 eps))) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps eps)) eps) (* -1/2 x) (/ (* (neg (* eps eps)) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x))) (neg eps)) (- (* 1/24 (* eps eps)) 1/2) (- (* (* eps eps) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/2 eps) (/ (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (+ (* -1/2 (* (sin x) eps)) (cos x)) (* (cos x) (cos (* 1/2 eps))) (* eps eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (* -1/6 eps) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* (sin x) eps))

simplify190.0ms (1.4%)

Memory

19.0MiB live, 157.7MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	556	2389
1	2180	2265
0	8225	2076

Stop Event

1×	iter limit
1×	node limit

Counts

151 → 150

Calls

Call 1

Inputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 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)))))))
(+ (* 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))))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1/2 x)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 3) x)))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (* (pow eps 2) x)) (* 1/2 (pow eps 3)))))
(+ (* -1 (pow eps 2)) (* x (+ (* 1/2 (pow eps 3)) (* x (+ (* -1/12 (* (pow eps 3) x)) (* 1/2 (pow eps 2)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))))
(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
(+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 2) (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (cos x) (cos (* 1/2 eps)))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(cos (+ x (* 1/2 eps)))
(cos (* -1/2 (+ eps (* 2 x))))
(* eps (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* 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)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (* eps x))))
-1/2
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/12 (pow eps 2)) 1/2)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(pow eps 2)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/6 eps)
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* 1/2 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(cos (- x (* -1/2 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 #s(literal 2 binary64) (.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)))))
(+ (* 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)))))))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal 2 binary64) (.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))))))
(+ (* 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))))))))))
(fma.f64 #s(literal 2 binary64) (.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)))) (.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 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 #s(literal 2 binary64) (.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)))))
(+ (* 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)))))))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal 2 binary64) (.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))))))
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(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
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1
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(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
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(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
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(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
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(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(* -1/2 (* (pow eps 2) x))
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(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
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(* eps (sin x))
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(cos (- (* 1/2 eps) (* -1 x)))
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(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
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(* eps (cos x))
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(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 eps #s(literal -1/4 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(cos x)
(cos.f64 x)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* 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)
(* eps (+ 1 (* -1/2 (* eps x))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow eps 2)) 1/2)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(- (* 1/12 (pow eps 2)) 1/2)
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (-.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)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.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)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (-.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)) (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(* -1 (* (pow eps 2) (cos x)))
(.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))
(* (pow eps 2) (+ (* -1 (cos x)) (* 1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps (neg.f64 (cos.f64 x))) (*.f64 eps eps))
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal 1/384 binary64) (.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 eps eps) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/46080 binary64) (.f64 eps eps) #s(literal 1/384 binary64))) (.f64 eps eps) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) (*.f64 eps eps) (cos.f64 x))
(pow eps 2)
(*.f64 eps eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(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))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(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))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps)
(* 1/24 (* (pow eps 4) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)) (sin.f64 x))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 4 binary64)))
(* 1/24 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))) eps) eps)
(* 1/12 (pow eps 2))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))) eps) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* 1/2 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (sin.f64 x)) #s(literal 1/2 binary64))
(* (pow eps 3) (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (neg.f64 (cos.f64 x)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* 1/24 (* (pow eps 3) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 3 binary64)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* (pow eps 3) (+ (* -1/2 (sin x)) (/ (cos x) eps))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (neg.f64 (cos.f64 x)) eps)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(.f64 (neg.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/24 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (neg.f64 eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (neg.f64 (cos.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite222.0ms (1.7%)

Memory

-9.4MiB live, 140.1MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	494
0	136	482
1	551	410
2	4862	410
0	8216	401

Stop Event

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

Counts

27 → 441

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 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 eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 eps eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (sin.f64 x) eps)

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

eval147.0ms (1.1%)

Memory: -29.1MiB live, 106.0MiB allocated; 11ms collecting garbage
Compiler: Compiled 36 316 to 3 875 computations (89.3% saved)

prune61.0ms (0.5%)

Memory

9.7MiB live, 66.2MiB allocated; 5ms collecting garbage

Pruning

38 alts after pruning (30 fresh and 8 done)

	Pruned	Kept	Total
New	695	13	708
Fresh	7	17	24
Picked	2	3	5
Done	0	5	5
Total	704	38	742

Accuracy

100.0%

Counts

742 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.3%	(fma.f64 (sin.f64 x) #s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
	62.6%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
✓	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) #s(approx (* (sin (/ eps -2)) (sin (* x -1))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64))) eps))))
	99.8%	(.f64 (.f64 #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(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.5%	(.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))))
✓	98.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (.f64 #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))))
	99.5%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	50.6%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
	50.3%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
	50.6%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
	50.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
	50.9%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.5%	#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))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.0%	#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))
	50.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	47.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	6.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
✓	96.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
	97.4%	#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)))
✓	96.1%	#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 eps) eps)))
	6.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
	99.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (/.f64 (+.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
✓	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	97.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))

Compiler

Compiled 3 512 to 1 395 computations (60.3% saved)

regimes43.0ms (0.3%)

Memory

24.9MiB live, 24.9MiB allocated; 0ms collecting garbage

Counts

58 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 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 (-.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(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 (-.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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#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))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (.f64 #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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.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) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 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))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (+.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#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))
(fma.f64 (sin.f64 x) #s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) #s(approx (* (sin (/ eps -2)) (sin (* x -1))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64))) eps))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (/.f64 (+.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.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)))))

Outputs

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

Calls

3 calls:

13.0ms	x
13.0ms	eps
13.0ms	(-.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)

regimes46.0ms (0.3%)

Memory

-5.9MiB live, 41.4MiB allocated; 2ms collecting garbage

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 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 (-.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(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 (-.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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#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))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (.f64 #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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.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) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 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))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (+.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#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))
(fma.f64 (sin.f64 x) #s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) #s(approx (* (sin (/ eps -2)) (sin (* x -1))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) eps #s(literal -1/2 binary64))) eps))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))

Outputs

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

Calls

3 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x
12.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes66.0ms (0.5%)

Memory

-13.7MiB live, 30.9MiB allocated; 3ms collecting garbage

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 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 (-.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(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 (-.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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#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))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (sin.f64 (.f64 #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

#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))))

Calls

3 calls:

45.0ms	eps
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated; 0ms collecting garbage

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 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 (-.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(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 (-.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(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) #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 (-.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(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes56.0ms (0.4%)

Memory

-21.8MiB live, 25.1MiB allocated; 2ms collecting garbage

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 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))))

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:

39.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

24.7MiB live, 24.7MiB allocated; 0ms collecting garbage

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (+ (* -1/2 (* (sin x) eps)) (cos x)) (neg (* eps eps))) (.f64 (.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 eps)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #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))))

Outputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes76.0ms (0.6%)

Memory

-43.9MiB live, 17.0MiB allocated; 57ms collecting garbage

Counts

25 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) (*.f64 #s(literal -1/6 binary64) eps)) eps (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:

61.0ms	eps
6.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
98.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.0%	1	`x`
98.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory

22.7MiB live, 22.7MiB allocated; 0ms collecting garbage

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

-19.6MiB live, 28.7MiB allocated; 4ms collecting garbage

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))

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

Calls

3 calls:

11.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

23.1MiB live, 23.1MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) #s(literal -1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) eps) eps)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/24 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) (neg.f64 eps)) (*.f64 (neg.f64 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #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 (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.5%	1	`x`
97.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.2%)

Memory

-30.4MiB live, 15.6MiB allocated; 2ms collecting garbage

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))

Calls

3 calls:

24.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos 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 eps)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#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 eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) 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 #s(literal 1/12 binary64) (.f64 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 (.f64 #s(approx (+ ( -1/2 (* (sin x) eps)) (cos x)) (fma.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) (neg.f64 (.f64 eps eps))) (neg.f64 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:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.4%	1	`x`
97.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.2%	1	`x`
96.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Accuracy

Total -57.7b remaining (-2350.6%)

Threshold costs -57.7b (-2350.6%)

Counts

3 → 1

Calls

Call 1

Inputs

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

#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 eps) eps)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.2%	1	`x`
96.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify65.0ms (0.5%)

Memory

-32.6MiB live, 65.7MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	474
1	240	467
2	571	464
3	2181	464
4	6902	464

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.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) (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))))
(.f64 (.f64 #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(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)) #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 #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))))
#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 (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) 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) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (/ eps -2)) (cos (* x -1))) (* (sin (/ eps -2)) (sin (* x -1))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.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) (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))))
(.f64 (.f64 #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(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)) #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 #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))))
#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 (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* 1/12 (* eps eps)) 1/2) #s(literal -1/2 binary64)) x (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (.f64 #s(literal -1/6 binary64) eps) 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) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* (cos x) eps) -1/6)) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))

derivations1.4s (10.5%)

Memory

26.7MiB live, 864.8MiB allocated; 107ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267
0	40	218
0	71	204
1	281	204
2	2538	204
0	8507	204
0	556	2389
1	2180	2265
0	8225	2076
0	495	2059
1	1859	1970
2	7019	1956
0	8345	1788
0	585	2543
1	2187	2411
0	8393	2213
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Compiler

Compiled 488 to 153 computations (68.6% saved)

preprocess81.0ms (0.6%)

Memory: 27.6MiB live, 122.4MiB allocated; 16ms collecting garbage
Compiler: Compiled 1 020 to 344 computations (66.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze47.0ms (0.4%)

sample7.6s (57.7%)

explain97.0ms (0.7%)

preprocess47.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize28.0ms (0.2%)

series4.0ms (0%)

simplify143.0ms (1.1%)

rewrite162.0ms (1.2%)

eval73.0ms (0.6%)

prune10.0ms (0.1%)

simplify109.0ms (0.8%)

localize187.0ms (1.4%)

series34.0ms (0.3%)

simplify177.0ms (1.3%)

rewrite225.0ms (1.7%)

eval75.0ms (0.6%)

prune35.0ms (0.3%)

simplify153.0ms (1.2%)

localize266.0ms (2%)

series42.0ms (0.3%)

simplify176.0ms (1.3%)

rewrite229.0ms (1.7%)

eval116.0ms (0.9%)

prune68.0ms (0.5%)

simplify108.0ms (0.8%)

localize323.0ms (2.5%)

series38.0ms (0.3%)

simplify190.0ms (1.4%)

rewrite222.0ms (1.7%)

eval147.0ms (1.1%)

prune61.0ms (0.5%)

regimes43.0ms (0.3%)

regimes46.0ms (0.3%)

regimes66.0ms (0.5%)

regimes28.0ms (0.2%)

regimes56.0ms (0.4%)

regimes22.0ms (0.2%)

regimes76.0ms (0.6%)

regimes19.0ms (0.1%)

regimes23.0ms (0.2%)

regimes17.0ms (0.1%)

regimes31.0ms (0.2%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

simplify65.0ms (0.5%)

derivations1.4s (10.5%)

preprocess81.0ms (0.6%)

end0.0ms (0%)

Profiling