Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze67.0ms (0.6%)

Memory

-7.5MiB live, 83.3MiB allocated; 23ms 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)

sample6.8s (56.1%)

Memory

-249.3MiB live, 7 492.2MiB allocated; 2.2s collecting garbage

Samples

3.4s	25 643×	0	invalid
1.0s	5 126×	1	valid
396.0ms	3 130×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.6s

const: 844.0ms (23.2% of total)

ival-sin: 804.0ms (22.1% of total)

ival-<: 311.0ms (8.5% of total)

ival-<=: 299.0ms (8.2% of total)

ival-add: 283.0ms (7.8% of total)

ival-mult: 257.0ms (7.1% of total)

ival-sub: 247.0ms (6.8% of total)

ival-fabs: 223.0ms (6.1% of total)

adjust: 206.0ms (5.7% of total)

ival-and: 109.0ms (3% of total)

exact: 46.0ms (1.3% of total)

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

Bogosity

explain110.0ms (0.9%)

Memory

16.0MiB live, 119.8MiB allocated; 12ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
227	1	(6.684622507753595e-264 6.067263533790162e-266)	2	(-3.454990883413934e-238 3.9539246232771345e-240)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
4	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	226	4
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	4	0

Confusion

	Predicted +	Predicted -
+	227	2
-	1	26

Precision

0.9956140350877193

Recall

0.9912663755458515

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	227	2	0
-	1	2	24

Precision?

0.9870689655172413

Recall?

1.0

Freqs

test

number	freq
0	28
1	226
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms	336×	1	valid
22.0ms	176×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-sin: 16.0ms (46.3% of total)

adjust: 10.0ms (29% of total)

ival-add: 4.0ms (11.6% of total)

ival-sub: 4.0ms (11.6% of total)

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

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

preprocess93.0ms (0.8%)

Memory

-15.8MiB live, 29.1MiB allocated; 5ms 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	50	43
5	78	43
6	137	43
7	382	43
8	1447	43
9	5227	43
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

2.7MiB live, 2.7MiB 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)

localize30.0ms (0.2%)

Memory

32.1MiB live, 32.1MiB 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	0.1746749880282053	(sin.f64 (+.f64 x eps))
accuracy	24.38699009277732	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

19.0ms	168×	1	valid
4.0ms	88×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sin: 6.0ms (39.3% of total)

adjust: 5.0ms (32.7% of total)

ival-add: 2.0ms (13.1% of total)

ival-sub: 2.0ms (13.1% of total)

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

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

series4.0ms (0%)

Memory

2.3MiB live, 2.3MiB 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))

simplify174.0ms (1.4%)

Memory

-34.4MiB live, 107.8MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1254	296
3	4271	296
0	8150	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)))

rewrite182.0ms (1.5%)

Memory

36.0MiB live, 128.7MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 158

Calls

Call 1

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

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

eval80.0ms (0.7%)

Memory: -32.3MiB live, 22.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 5 640 to 740 computations (86.9% saved)

prune8.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	10	182

Accuracy

100.0%

Counts

182 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.9%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
▶	37.1%	(/.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))))
	36.5%	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
▶	61.9%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
✓	61.6%	(-.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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.0%	#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))
▶	98.8%	#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))
▶	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 501 to 220 computations (56.1% saved)

simplify126.0ms (1%)

Memory

-11.6MiB live, 34.1MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (+.f64 eps x))
cost-diff	0	(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
cost-diff	0	(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
cost-diff	10	(/.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))))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	0	(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
cost-diff	0	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
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 (.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	1	(cos.f64 (/.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: 0 (0.0ms)

Iter	Nodes	Cost
0	37	217
0	65	207
1	118	207
2	278	204
3	886	204
4	3185	194
0	8133	192

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

localize188.0ms (1.6%)

Memory

21.3MiB live, 67.4MiB allocated; 1ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.213222509768442	(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
accuracy	0.24609375	(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
accuracy	12.540347119725714	(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
accuracy	27.261825083011527	(/.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))))
accuracy	0.0	(cos.f64 eps)
accuracy	0.0078125	(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
accuracy	0.01953125	(*.f64 (sin.f64 eps) (cos.f64 x))
accuracy	24.38699009277732	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
accuracy	0.0078125	(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	0.0234375	(*.f64 (sin.f64 x) eps)
accuracy	0.7864239630799743	#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	2.958749351561334	#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	0.0234375	(.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	0.15970553043532218	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

135.0ms	173×	1	valid
20.0ms	81×	0	valid
5.0ms	2×	3	valid

Compiler

Compiled 213 to 39 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-cos: 49.0ms (36.6% of total)

adjust: 23.0ms (17.2% of total)

ival-mult: 16.0ms (11.9% of total)

ival-sin: 16.0ms (11.9% of total)

ival-add: 11.0ms (8.2% of total)

ival-pow2: 7.0ms (5.2% of total)

ival-div: 6.0ms (4.5% of total)

ival-sub: 5.0ms (3.7% of total)

exact: 1.0ms (0.7% of total)

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

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

series62.0ms (0.5%)

Memory

-27.6MiB live, 17.7MiB allocated; 5ms collecting garbage

Counts

22 → 138

Calls

Call 1

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

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))))))
(* -1/2 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)))))))
(+ (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))))))))
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 (- (* 2 (cos eps)) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))
(pow (sin eps) 2)
(+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2))) 1)))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))))) (pow (sin eps) 2))
(+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2)))))) (pow (sin eps) 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)))))))
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -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))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos eps) (sin x)) (* (cos x) (sin eps)))
(sin x)
(/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x))))
(- (pow (sin (+ eps x)) 2) (pow (sin x) 2))
(pow (sin (+ eps x)) 2)
(sin (+ eps x))
(* (cos x) (sin eps))
(+ (sin x) (sin (+ eps x)))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(/ (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- eps (* -1 x)))))
(- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2))
(pow (sin (- eps (* -1 x))) 2)
(sin (- eps (* -1 x)))
(+ (sin x) (sin (- eps (* -1 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))))))
(* 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)) (* -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 (* -1/6 (pow eps 2))))
(* 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)
(+ (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))))))))
(+ 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)))
(* eps (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))
(* 2 (* eps (* (cos x) (sin x))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))
(* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))
(pow (sin x) 2)
(+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))
(+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))
(* 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 (+ 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) (* -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))))))))
(* 2 (sin x))
(+ (* 2 (sin x)) (* eps (cos x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -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)))
(cos eps)
(sin (* 1/2 eps))
(* 2 (sin (* 1/2 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 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 (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))
(- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))
(pow (sin (- x (* -1 eps))) 2)
(sin (- x (* -1 eps)))
(+ (sin x) (sin (- x (* -1 eps))))

Calls

6 calls:

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

simplify253.0ms (2.1%)

Memory

27.3MiB live, 120.1MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	545	2332
1	2019	2263
0	8051	2092

Stop Event

1×	iter limit
1×	node limit

Counts

138 → 136

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

rewrite124.0ms (1%)

Memory

-9.4MiB live, 84.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	177
0	65	145
1	288	145
0	2285	145

Stop Event

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

Counts

22 → 354

Calls

Call 1

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

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

eval119.0ms (1%)

Memory: -37.5MiB live, 98.8MiB allocated; 30ms collecting garbage
Compiler: Compiled 12 584 to 1 793 computations (85.8% saved)

prune19.0ms (0.2%)

Memory

0.2MiB live, 47.5MiB allocated; 1ms collecting garbage

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	434	15	449
Fresh	2	2	4
Picked	3	2	5
Done	0	1	1
Total	439	20	459

Accuracy

100.0%

Counts

459 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.9%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
✓	61.9%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
	61.5%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 x))
✓	61.6%	(-.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 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))))))
	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))))
▶	99.4%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	98.8%	#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 (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))
	96.3%	#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))
▶	96.3%	#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))
	5.8%	#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))
▶	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
	96.4%	#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)))
	95.4%	#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 eps) eps)))
	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) eps)))
	99.7%	#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 912 to 642 computations (29.6% saved)

simplify120.0ms (1%)

Memory

8.3MiB live, 150.1MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	463
0	103	443
1	180	428
2	504	423
3	2240	422
4	5609	422
0	8426	408

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 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(*.f64 (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 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))
(cos.f64 (*.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
(.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
(sin.f64 (/.f64 eps #s(literal -2 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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 x eps)
x
eps
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)
(.f64 eps (.f64 eps eps))
eps
(*.f64 eps eps)
(-.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))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)
(.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
#s(literal 1/1920 binary64)
#s(literal 1/24 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)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

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 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(.f64 (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 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
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)))))
(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 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))
(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)
(cos.f64 (/.f64 eps #s(literal -2 binary64)))
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps))
(/.f64 eps #s(literal -2 binary64))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -2 binary64)
(.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (*.f64 x #s(literal -1 binary64)))
(neg.f64 (sin.f64 x))
(sin.f64 (/.f64 eps #s(literal -2 binary64)))
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps))
#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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 x eps)
x
eps
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (fma.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)))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (fma.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))
(fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)
(fma.f64 (fma.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)
(.f64 eps (.f64 eps eps))
(pow.f64 eps #s(literal 3 binary64))
eps
(*.f64 eps eps)
(-.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))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps #s(literal -1/24 binary64))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)
(.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
#s(literal 1/1920 binary64)
#s(literal 1/24 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

localize239.0ms (2%)

Memory

10.0MiB live, 414.0MiB allocated; 59ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(.f64 eps (.f64 eps eps))
accuracy	0.1171875	(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)
accuracy	0.15970553043532218	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.26720602641881314	#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
accuracy	0.0078125	(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
accuracy	0.015625	(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.7864239630799743	#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))
accuracy	2.9041579007667697	#s(approx (* (sin x) eps) (*.f64 x eps))
accuracy	0.0078125	(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.015625	(.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)
accuracy	0.7864239630799743	#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))
accuracy	2.331495412645659	#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)))
accuracy	0.015625	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.7864239630799743	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
accuracy	2.9804340930301367	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
accuracy	0.0078125	(.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))
accuracy	0.01171875	(-.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)))))
accuracy	0.01953125	(.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
accuracy	0.0234375	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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))))))

Samples

139.0ms	168×	1	valid
32.0ms	88×	0	valid

Compiler

Compiled 354 to 54 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-mult: 42.0ms (32.3% of total)

adjust: 25.0ms (19.2% of total)

ival-sin: 15.0ms (11.5% of total)

const: 13.0ms (10% of total)

ival-add: 11.0ms (8.5% of total)

ival-cos: 11.0ms (8.5% of total)

ival-div: 6.0ms (4.6% of total)

ival-sub: 5.0ms (3.8% of total)

exact: 1.0ms (0.8% of total)

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

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

series42.0ms (0.3%)

Memory

35.6MiB live, 78.7MiB allocated; 12ms collecting garbage

Counts

24 → 99

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.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 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))
#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))
(.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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(.f64 eps (.f64 eps eps))
(-.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))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)

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 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)))))))
(* -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))))))))))
(* -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))))))))
(- (* (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))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* eps (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ 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 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(pow eps 3)
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(* 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)))))))))))
(* -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))))))))
(* 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))))
(* 1/1920 (pow eps 2))
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2))))
(* -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)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	x	@	-inf	((+ 0 eps) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2)))) (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)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps (* eps eps)) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (sin (* x -1)) (sin (/ eps -2))) (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps))
5.0ms	eps	@	inf	((+ 0 eps) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2)))) (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)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps (* eps eps)) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (sin (* x -1)) (sin (/ eps -2))) (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps))
5.0ms	eps	@	-inf	((+ 0 eps) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2)))) (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)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps (* eps eps)) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (sin (* x -1)) (sin (/ eps -2))) (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps))
4.0ms	x	@	inf	((+ 0 eps) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2)))) (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)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps (* eps eps)) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (sin (* x -1)) (sin (/ eps -2))) (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps))
3.0ms	eps	@	0	((+ 0 eps) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2)))) (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)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps (* eps eps)) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (sin (* x -1)) (sin (/ eps -2))) (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps))

simplify229.0ms (1.9%)

Memory

2.8MiB live, 250.9MiB allocated; 98ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	381	1335
1	1401	1243
2	5526	1229
0	8499	1128

Stop Event

1×	iter limit
1×	node limit

Counts

99 → 98

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 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)))))))
(* -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))))))))))
(* -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))))))))
(- (* (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))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* eps (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(* (sin (* -1 x)) (sin (* -1/2 eps)))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ 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 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(pow eps 3)
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(* 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)))))))))))
(* -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))))))))
(* 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))))
(* 1/1920 (pow eps 2))
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2))))
(* -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)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ 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)))
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1
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(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
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(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
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(* -1 x)
(neg.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
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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)
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(+ 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))))
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(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 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 eps) x) #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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(* -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)))))
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(- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))
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(cos (* -1 x))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(+ (cos x) (* -1/2 (* eps (sin x))))
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(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(.f64 (.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) x)
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(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
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(* (sin (* -1 x)) (sin (* -1/2 eps)))
(.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* (cos (* -1 x)) (cos (* -1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
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(cos (* -1/2 (- eps (* -2 x))))
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(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
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(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
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(* eps (cos x))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(cos x)
(cos.f64 x)
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(pow eps 3)
(pow.f64 eps #s(literal 3 binary64))
-1/24
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(* eps (cos (* -1 x)))
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(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
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(* eps (+ 1 (* -1/24 (pow eps 2))))
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(- (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 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)

rewrite111.0ms (0.9%)

Memory

4.8MiB live, 144.6MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	318
0	101	287
1	336	278
0	3034	272

Stop Event

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

Counts

24 → 338

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(-.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 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))
#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))
(.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) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(.f64 eps (.f64 eps eps))
(-.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))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)

Outputs
(/.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps (neg.f64 eps)))
(/.f64 (fma.f64 (.f64 eps (neg.f64 eps)) #s(literal 2 binary64) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (*.f64 (neg.f64 eps) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 (.f64 eps eps) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (.f64 #s(literal 2 binary64) (.f64 eps (neg.f64 eps)))) (*.f64 #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 #s(literal 2 binary64) (.f64 eps eps)))
(/.f64 (*.f64 eps (neg.f64 eps)) (neg.f64 eps))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps)))
(/.f64 (*.f64 eps eps) eps)
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(-.f64 eps #s(literal 0 binary64))
(+.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 #s(literal 1 binary64) x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) #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))) (sin.f64 (neg.f64 x))) #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 (neg.f64 (*.f64 (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))))) (neg.f64 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x)))))
(/.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 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))) (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 (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)))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (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)))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (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)))) (-.f64 (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))))) #s(literal 2 binary64))
(/.f64 (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
(/.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))) (sin.f64 (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))) (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) 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 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (sin.f64 (neg.f64 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 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)) (.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 (neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (sin.f64 (neg.f64 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)))))
(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 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #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 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x)))) (/.f64 (pow.f64 (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) #s(literal 2 binary64)) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))) (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))) (sin.f64 (neg.f64 x))) #s(literal 3 binary64)) (fma.f64 (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x))) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))) (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 (neg.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))) (sin.f64 (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))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (*.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 (neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64)))) (sin.f64 (neg.f64 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)))))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (neg.f64 x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal 1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (*.f64 #s(literal 1 binary64) x)))
(cos.f64 (*.f64 #s(literal 1 binary64) x))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 (neg.f64 x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))
(neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))
(neg.f64 x)
(+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 x #s(literal -2 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)
(.f64 eps #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 eps (neg.f64 eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) (*.f64 eps (neg.f64 eps))) (neg.f64 eps))
(/.f64 (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))))
(fma.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)) #s(literal 0 binary64)))
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(fma.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))))
(fma.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(+.f64 (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(+.f64 (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))))
(+.f64 (.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)) #s(literal 0 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#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))
(.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)
(.f64 eps #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))))
(/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #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)))) (.f64 eps eps))
(/.f64 (.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))) (.f64 eps (neg.f64 eps))) (neg.f64 eps))
(/.f64 (.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))) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
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(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64)))
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(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
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(fma.f64 (.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 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (/.f64 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 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))) (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (neg.f64 x)))
(*.f64 (sin.f64 (neg.f64 x)) (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(/.f64 (neg.f64 (-.f64 (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))))) #s(literal -2 binary64))
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(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (neg.f64 x))) (sin.f64 (+.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (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))))) #s(literal 2 binary64))
(/.f64 (+.f64 (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))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))) (cos.f64 (+.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) x))) (cos.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x))) (cos.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (.f64 #s(literal 1 binary64) x))) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 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 (*.f64 #s(literal 1 binary64) x) (/.f64 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 (neg.f64 x) (/.f64 eps #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (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)))) #s(literal 2 binary64))
(neg.f64 (/.f64 (+.f64 (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)))) #s(literal -2 binary64)))
(+.f64 (/.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))) #s(literal 2 binary64)))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (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))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (fabs.f64 eps)) (fabs.f64 eps))
(.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps)
(.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)))
(.f64 eps (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/322560 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1/3686400 binary64)) (.f64 eps eps)) (-.f64 (.f64 #s(literal -1/322560 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/33560740233216000 binary64) (pow.f64 (.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/7077888000 binary64)) (.f64 eps eps)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/322560 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1/3686400 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/619315200 binary64))))
(/.f64 (.f64 (.f64 eps (neg.f64 eps)) (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)) (.f64 eps eps))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) (.f64 eps (neg.f64 eps))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (fabs.f64 eps)) (fabs.f64 eps) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (fabs.f64 eps)) (fabs.f64 eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps))
(fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) (.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps)))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))

eval65.0ms (0.5%)

Memory: -0.6MiB live, 93.8MiB allocated; 12ms collecting garbage
Compiler: Compiled 15 407 to 1 879 computations (87.8% saved)

prune23.0ms (0.2%)

Memory

-1.3MiB live, 43.0MiB allocated; 6ms collecting garbage

Pruning

25 alts after pruning (19 fresh and 6 done)

	Pruned	Kept	Total
New	401	10	411
Fresh	3	9	12
Picked	2	3	5
Done	0	3	3
Total	406	25	431

Accuracy

100.0%

Counts

431 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
✓	61.9%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
	61.5%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 x))
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	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))))
	99.4%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.3%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	52.8%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
✓	98.8%	#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 (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))
	96.3%	#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))
✓	96.3%	#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))
	5.8%	#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))
	96.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
▶	50.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
▶	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
✓	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
▶	96.4%	#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)))
	95.4%	#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 eps) eps)))
	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) eps)))
▶	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.7%	#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 1 367 to 920 computations (32.7% saved)

simplify110.0ms (0.9%)

Memory

7.0MiB live, 101.4MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
cost-diff	0	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (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 eps (.f64 eps eps))
cost-diff	0	#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
cost-diff	0	#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
cost-diff	0	(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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	88	648
0	124	634
1	243	631
2	777	627
3	4069	627
0	8204	602

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(literal 2 binary64)
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(sin.f64 x)
x
(.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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 x eps))
eps
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
(fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
eps
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(*.f64 x x)
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)
(.f64 eps (.f64 eps eps))
eps
(*.f64 eps eps)
#s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64))
#s(literal -1/24 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)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (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))) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(.f64 (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))) #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
(sin.f64 x)
x
(.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)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #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 (+.f64 x eps)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 x eps))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x) x))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps)
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x) x))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x) x)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x) x))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(.f64 (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x) x)
(-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
(fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
eps
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(*.f64 x x)
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (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)) #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)
(fma.f64 #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(.f64 eps (.f64 eps eps))
(pow.f64 eps #s(literal 3 binary64))
eps
(*.f64 eps eps)
#s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64))
#s(literal -1/24 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)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

localize343.0ms (2.8%)

Memory

-10.3MiB live, 505.8MiB allocated; 108ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(.f64 eps (.f64 eps eps))
accuracy	0.15970553043532218	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.26720602641881314	#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
accuracy	0.7047567244422347	#s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64))
accuracy	0.16015625	(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
accuracy	0.7864239630799743	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
accuracy	2.331495412645659	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
accuracy	28.504208865590787	(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
accuracy	0.0078125	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
accuracy	0.1328125	(*.f64 eps (+.f64 x eps))
accuracy	0.7864239630799743	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
accuracy	2.3183509542517426	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
accuracy	0.015625	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
accuracy	0.7864239630799743	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
accuracy	2.331495412645659	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
accuracy	61.6340394859646	#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
accuracy	0.0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.0078125	(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.01171875	(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.0234375	(.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))

Samples

234.0ms	168×	1	valid
53.0ms	88×	0	valid

Compiler

Compiled 389 to 77 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 242.0ms

ival-mult: 120.0ms (49.6% of total)

adjust: 38.0ms (15.7% of total)

ival-add: 19.0ms (7.9% of total)

const: 16.0ms (6.6% of total)

ival-sin: 14.0ms (5.8% of total)

ival-cos: 14.0ms (5.8% of total)

ival-div: 11.0ms (4.5% of total)

ival-sub: 8.0ms (3.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series44.0ms (0.4%)

Memory

9.2MiB live, 57.9MiB allocated; 15ms collecting garbage

Counts

26 → 135

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 eps (.f64 eps eps))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 eps (+.f64 x eps))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
#s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

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
(+ 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)))))
(* -1/2 x)
(* -1/2 eps)
(+ (* -1 x) (* -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))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (* eps x))) (pow x 2))
(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))))))
(* 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)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos x) (cos (* 1/2 eps)))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (/ 1 x)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (/ (- (* 1/2 eps) (/ 1 x)) 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)))))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(pow eps 3)
(* 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))))
(+ (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)))))))
(* eps (+ eps x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+ (* -1/2 (* eps x)) (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(+ (* -1/2 (/ eps x)) (/ 1 (pow x 2)))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(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)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* eps (+ (* -1/2 x) (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)))
(* eps (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 x))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)) (* 1/2 x))))
(* -1 (* eps (- (* 1/2 (/ 1 x)) (/ 1 (* eps (pow x 2))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	0	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (* eps (* eps eps)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (cos x) (cos (* 1/2 eps))) (* eps (+ x eps)) (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (/ (+ (* -1/2 eps) (/ 1 x)) x) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)))
7.0ms	eps	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (* eps (* eps eps)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (cos x) (cos (* 1/2 eps))) (* eps (+ x eps)) (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (/ (+ (* -1/2 eps) (/ 1 x)) x) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)))
7.0ms	eps	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (* eps (* eps eps)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (cos x) (cos (* 1/2 eps))) (* eps (+ x eps)) (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (/ (+ (* -1/2 eps) (/ 1 x)) x) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)))
6.0ms	x	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (* eps (* eps eps)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (cos x) (cos (* 1/2 eps))) (* eps (+ x eps)) (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (/ (+ (* -1/2 eps) (/ 1 x)) x) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)))
6.0ms	x	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (* (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (sin (* 1/2 eps))) (* 2 (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps))))) (+ (* (sin (* -1/2 eps)) (sin x)) (* (cos x) (cos (* 1/2 eps)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (* eps (* eps eps)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (* (cos x) (cos (* 1/2 eps))) (* eps (+ x eps)) (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (/ (+ (* -1/2 eps) (/ 1 x)) x) (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) (cos (/ (+ (* 2 x) eps) -2)))

simplify138.0ms (1.1%)

Memory

18.3MiB live, 155.5MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	461	1847
1	1761	1744
2	6768	1737
0	8368	1600

Stop Event

1×	iter limit
1×	node limit

Counts

135 → 134

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
(+ 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)))))
(* -1/2 x)
(* -1/2 eps)
(+ (* -1 x) (* -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))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (* eps x))) (pow x 2))
(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))))))
(* 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)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (cos x) (cos (* 1/2 eps)))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (/ 1 x)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (/ (- (* 1/2 eps) (/ 1 x)) 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)))))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(pow eps 3)
(* 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))))
(+ (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)))))))
(* eps (+ eps x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+ (* -1/2 (* eps x)) (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(+ (* -1/2 (/ eps x)) (/ 1 (pow x 2)))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(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)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* eps (+ (* -1/2 x) (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)))
(* eps (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 x))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)) (* 1/2 x))))
(* -1 (* eps (- (* 1/2 (/ 1 x)) (/ 1 (* eps (pow x 2))))))
(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 (.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 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(+ (* 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 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (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 (.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 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(+ (* 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 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))))
(* 2 (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* 2 (cos (* 1/2 eps))) (* 2 (* x (sin (* -1/2 eps)))))
(.f64 (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))) (* x (+ (* -1 (* x (cos (* 1/2 eps)))) (* 2 (sin (* -1/2 eps))))))
(fma.f64 (.f64 (neg.f64 x) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (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))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps)))))))))
(fma.f64 (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 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))))))
(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 (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* 1/2 eps)))))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (.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)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* -1/6 (* x (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)))
(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)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (+.f64 x eps) (.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 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.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))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.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 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (pow.f64 x #s(literal 4 binary64)) (.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)))))
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow eps 2))
(*.f64 (+.f64 x eps) eps)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -1/2 (* eps x))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) x)
(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 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (.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)) (* 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)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos (* -1 x)) (cos (* -1/2 eps))) (* (sin (* -1 x)) (sin (* -1/2 eps))))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (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))))
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (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))))
(* 2 (+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))
(.f64 (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))) #s(literal 2 binary64))
(+ (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* -1/2 eps))))
(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)))
(- (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))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(.f64 (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(.f64 (.f64 (fma.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.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)))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(* eps x)
(*.f64 x eps)
(* x (+ eps (/ (pow eps 2) x)))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(/ (+ (* -1/2 eps) (/ 1 x)) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1 binary64) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 eps x)) x)) (.f64 x x))
(* -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)))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1 (/ (- (* 1/2 eps) (/ 1 x)) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) (neg.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 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) 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 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos 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)
(* 2 (cos x))
(*.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(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 #s(literal -1/4 binary64) eps) (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 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) 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)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) eps)
(pow eps 3)
(pow.f64 eps #s(literal 3 binary64))
(* 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 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #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 (fma.f64 (.f64 #s(literal 1/1920 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)) 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 #s(literal -1/8 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/46080 binary64) (.f64 eps eps) #s(literal 1/384 binary64)))))
(* eps (+ eps x))
(*.f64 (+.f64 x eps) eps)
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(+ (* -1/2 (* eps x)) (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))
(fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (/ eps x)) (/ 1 (pow x 2)))
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
-1/24
#s(literal -1/24 binary64)
(- (* 1/1920 (pow eps 2)) 1/24)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(fma.f64 (.f64 #s(literal 1/1920 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) #s(literal 1/24 binary64)))
(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 #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))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (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)
(* -1/2 (* eps x))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(* -1/2 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #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))
(* (pow eps 2) (+ 1 (/ x eps)))
(.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps)
(* eps (+ (* -1/2 x) (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)))
(.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) (.f64 x x) (.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) eps) x)) x) eps)
(* -1/322560 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/322560 binary64)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(- (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))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal -1 binary64)) (neg.f64 eps))) eps) 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)))
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) eps)) (* 1/2 x))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (neg.f64 x) x) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) (.f64 #s(literal 1/2 binary64) x)))
(* -1 (* eps (- (* 1/2 (/ 1 x)) (/ 1 (* eps (pow x 2))))))
(.f64 (neg.f64 eps) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite154.0ms (1.3%)

Memory

-21.6MiB live, 118.8MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	543
0	124	520
1	456	487
0	4379	468

Stop Event

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

Counts

26 → 349

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 eps (.f64 eps eps))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps))
(.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 eps (+.f64 x eps))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x)
#s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

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

eval74.0ms (0.6%)

Memory: -3.1MiB live, 106.1MiB allocated; 17ms collecting garbage
Compiler: Compiled 23 837 to 2 323 computations (90.3% saved)

prune29.0ms (0.2%)

Memory

4.7MiB live, 51.8MiB allocated; 1ms collecting garbage

Pruning

29 alts after pruning (21 fresh and 8 done)

	Pruned	Kept	Total
New	462	11	473
Fresh	4	10	14
Picked	3	2	5
Done	0	6	6
Total	469	29	498

Accuracy

100.0%

Counts

498 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
✓	61.9%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
	61.5%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 x))
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	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))))
	99.4%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.3%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
	99.0%	(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	98.8%	#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 (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))
	96.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.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))
✓	96.3%	#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))
	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	5.8%	#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))
✓	50.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
	50.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) eps))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
	51.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
✓	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
	96.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
	95.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) eps)))
✓	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.7%	#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 2 468 to 970 computations (60.7% saved)

regimes78.0ms (0.6%)

Memory

-11.1MiB live, 34.8MiB allocated; 4ms collecting garbage

Counts

46 → 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (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))
#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 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.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))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 x))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
(-.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 (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.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 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (-.f64 (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 (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))

Outputs

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

54.0ms	x
11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	eps

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)

regimes31.0ms (0.3%)

Memory

27.5MiB live, 27.5MiB allocated; 0ms collecting garbage

Counts

42 → 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (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))
#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 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.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))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 x))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
(-.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

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x
10.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes35.0ms (0.3%)

Memory

-19.4MiB live, 26.6MiB 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (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))
#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 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.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))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)) (cos.f64 x))) (sin.f64 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:

14.0ms	eps
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.2%)

Memory

-21.2MiB live, 28.2MiB allocated; 6ms collecting garbage

Counts

35 → 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) (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))

Outputs

(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	x
8.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

33.4MiB live, 33.4MiB allocated; 0ms collecting garbage

Counts

30 → 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(approx (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) #s(literal 1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.3%	1	`x`
99.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

-14.6MiB live, 30.1MiB allocated; 4ms 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))

Outputs

(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))

Calls

3 calls:

10.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes70.0ms (0.6%)

Memory

-14.9MiB live, 31.3MiB allocated; 2ms collecting garbage

Counts

27 → 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x))))

Outputs

(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

55.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated; 0ms 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.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 (fma.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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 #s(approx (/ (+ ( -1/2 eps) (/ 1 x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 x x)))) 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 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (neg.f64 eps)) #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)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) #s(approx (* (- (/ (+ (* -1/2 eps) (/ 1 x)) x) 1/2) (* x x)) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x (.f64 (.f64 x eps) #s(literal -1/2 binary64)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x)))) 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 (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))

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

Calls

3 calls:

6.0ms	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)

regimes16.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.4%	1	`x`
96.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

6.8MiB live, 6.8MiB 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))

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

2 calls:

3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
96.4%	1	`x`
96.4%	1	`eps`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes9.0ms (0.1%)

Memory

-34.0MiB live, 12.3MiB allocated; 2ms collecting garbage

Counts

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

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

Calls

3 calls:

4.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps

Results

Accuracy	Segments	Branch
96.3%	1	`x`
96.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB 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 (+ x eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x eps) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) eps)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
95.4%	1	`eps`
95.4%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Accuracy

Total -57.9b remaining (-1956.6%)

Threshold costs -57.9b (-1956.6%)

Counts

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

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

Results

Accuracy	Segments	Branch
95.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
95.4%	1	`x`
95.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify66.0ms (0.5%)

Memory

-19.5MiB live, 30.3MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	134	406
1	209	400
2	494	400
3	2065	400
4	5602	400

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (- (* (cos (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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 (* x -1)) (cos (/ eps -2))) (* (sin (* x -1)) (sin (/ eps -2))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (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 (/.f64 eps #s(literal -2 binary64)) (neg.f64 x))))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) x)) (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)))
#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 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (+.f64 (neg.f64 eps) (PI.f64)) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (.f64 eps (.f64 eps eps)) #s(approx (- (* (* (+ (* -1/322560 (* eps eps)) 1/1920) eps) eps) 1/24) #s(literal -1/24 binary64)) eps)) #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 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ x eps)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (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 (11.5%)

Memory

13.3MiB live, 740.5MiB allocated; 171ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4478	16
0	8242	16
0	545	2332
1	2019	2263
0	8051	2092
0	107	303
1	366	303
2	1254	296
3	4271	296
0	8150	267
0	63	318
0	101	287
1	336	278
0	3034	272
0	461	1847
1	1761	1744
2	6768	1737
0	8368	1600
0	88	543
0	124	520
1	456	487
0	4379	468
0	381	1335
1	1401	1243
2	5526	1229
0	8499	1128
0	37	177
0	65	145
1	288	145
0	2285	145

Stop Event

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

Compiler

Compiled 416 to 140 computations (66.3% saved)

preprocess137.0ms (1.1%)

Memory: -26.6MiB live, 79.6MiB allocated; 9ms collecting garbage
Compiler: Compiled 876 to 318 computations (63.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze67.0ms (0.6%)

sample6.8s (56.1%)

explain110.0ms (0.9%)

preprocess93.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize30.0ms (0.2%)

series4.0ms (0%)

simplify174.0ms (1.4%)

rewrite182.0ms (1.5%)

eval80.0ms (0.7%)

prune8.0ms (0.1%)

simplify126.0ms (1%)

localize188.0ms (1.6%)

series62.0ms (0.5%)

simplify253.0ms (2.1%)

rewrite124.0ms (1%)

eval119.0ms (1%)

prune19.0ms (0.2%)

simplify120.0ms (1%)

localize239.0ms (2%)

series42.0ms (0.3%)

simplify229.0ms (1.9%)

rewrite111.0ms (0.9%)

eval65.0ms (0.5%)

prune23.0ms (0.2%)

simplify110.0ms (0.9%)

localize343.0ms (2.8%)

series44.0ms (0.4%)

simplify138.0ms (1.1%)

rewrite154.0ms (1.3%)

eval74.0ms (0.6%)

prune29.0ms (0.2%)

regimes78.0ms (0.6%)

regimes31.0ms (0.3%)

regimes35.0ms (0.3%)

regimes29.0ms (0.2%)

regimes23.0ms (0.2%)

regimes25.0ms (0.2%)

regimes70.0ms (0.6%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes6.0ms (0%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

simplify66.0ms (0.5%)

derivations1.4s (11.5%)

preprocess137.0ms (1.1%)

end0.0ms (0%)

Profiling