Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze47.0ms (0.4%)

Memory

-11.0MiB live, 71.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.3s (49.4%)

Memory

-201.7MiB live, 6 156.1MiB allocated

Samples

3.3s	26 089×	0	invalid
584.0ms	5 483×	0	valid
534.0ms	2 773×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

const: 719.0ms (23.7% of total)

ival-sin: 584.0ms (19.3% of total)

ival-add: 329.0ms (10.8% of total)

ival-mult: 285.0ms (9.4% of total)

ival-<=: 253.0ms (8.3% of total)

ival-fabs: 244.0ms (8% of total)

ival-sub: 230.0ms (7.6% of total)

ival-<: 164.0ms (5.4% of total)

ival-and: 100.0ms (3.3% of total)

adjust: 71.0ms (2.3% of total)

exact: 43.0ms (1.4% of total)

ival-assert: 12.0ms (0.4% of total)

Bogosity

explain89.0ms (0.7%)

Memory

-12.4MiB live, 114.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
227	2	(-3.462796699570995e-167 2.764054764814959e-169)	3	(-7.668690385135368e-163 1.2576926385947832e-164)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	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	6
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	225	3
-	2	26

Precision

0.9911894273127754

Recall

0.9868421052631579

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	225	3	0
-	2	4	22

Precision?

0.9743589743589743

Recall?

1.0

Freqs

test

number	freq
0	29
1	227

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms	346×	0	valid
16.0ms	166×	1	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-sin: 13.0ms (56.7% of total)

adjust: 3.0ms (13.1% of total)

ival-sub: 3.0ms (13.1% of total)

ival-add: 3.0ms (13.1% of total)

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

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

preprocess24.0ms (0.2%)

Memory

-9.3MiB live, 28.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

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
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

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	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	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)

localize24.0ms (0.2%)

Memory

-5.0MiB live, 32.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.06795130521664963	(sin.f64 (+.f64 x eps))
accuracy	23.7355517497389	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	173×	0	valid
9.0ms	83×	1	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (56% of total)

adjust: 2.0ms (18.7% of total)

ival-add: 2.0ms (18.7% of total)

ival-sub: 1.0ms (9.3% of total)

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

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

series4.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

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))

simplify165.0ms (1.3%)

Memory

9.8MiB live, 129.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	314	291
2	779	284
3	2842	284
4	6177	284
0	8125	253

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

rewrite172.0ms (1.4%)

Memory

-3.4MiB live, 148.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Counts

4 → 214

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

eval29.0ms (0.2%)

Memory: 1.7MiB live, 39.2MiB allocated
Compiler: Compiled 6 283 to 852 computations (86.4% saved)

prune8.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	227	8	235
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	227	9	236

Accuracy

100.0%

Counts

236 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.9%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
	37.1%	(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶	99.2%	#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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 271 to 194 computations (28.4% saved)

simplify325.0ms (2.6%)

Memory

-14.0MiB live, 68.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
cost-diff	0	(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
cost-diff	0	(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))
cost-diff	0	(.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)
cost-diff	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))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (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 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	235
0	65	225
1	107	225
2	217	225
3	484	225
4	715	225
5	1018	225
6	1249	225
7	1570	225
8	2457	225
9	3602	225
10	3823	225
11	3869	225
12	3946	225
13	4071	222
14	4447	222
15	4697	222
16	5044	222
17	5850	222
18	6136	222
19	6215	222
20	6282	222
21	6302	222
22	6438	222
23	6759	222
24	7213	222
25	7361	222
26	7469	222
27	7481	222
28	7481	222
0	8389	219

Stop Event

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

Calls

Call 1

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

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

localize190.0ms (1.5%)

Memory

-6.1MiB live, 167.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.0	(cos.f64 eps)
accuracy	0.0234375	(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
accuracy	23.746267026584487	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
accuracy	0.0078125	(.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)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.0234375	(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
accuracy	0.5221282684660586	#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))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.014872480164287516	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.7329763515270904	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	1.4830018777613097	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.0571568094868315	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

49.0ms	166×	0	valid
46.0ms	88×	1	valid
7.0ms	2×	3	valid

Compiler

Compiled 455 to 78 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 23.0ms (33% of total)

ival-sin: 12.0ms (17.2% of total)

ival-add: 11.0ms (15.8% of total)

adjust: 8.0ms (11.5% of total)

ival-cos: 7.0ms (10.1% of total)

const: 4.0ms (5.7% of total)

ival-div: 2.0ms (2.9% of total)

ival-sub: 2.0ms (2.9% of total)

ival-neg: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

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

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

series43.0ms (0.3%)

Memory

9.9MiB live, 45.1MiB allocated

Counts

22 → 121

Calls

Call 1

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

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 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)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(+ 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)))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 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))))
(* -1/2 (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(cos x)
(* eps (cos x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 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 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 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)))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(cos eps)
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 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)))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (cos x) (* (cos x) eps))
6.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (cos x) (* (cos x) eps))
6.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (cos x) (* (cos x) eps))
4.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (cos x) (* (cos x) eps))
4.0ms	eps	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (sin x) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (cos x) (* (cos x) eps))

simplify225.0ms (1.8%)

Memory

1.9MiB live, 159.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	438	1583
1	1321	1512
2	3644	1476
0	8196	1329

Stop Event

1×	iter limit
1×	node limit

Counts

121 → 119

Calls

Call 1

Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 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)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(+ 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)))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 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))))
(* -1/2 (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(cos x)
(* eps (cos x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 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 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 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)))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(cos eps)
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 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)))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(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 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.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 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (.f64 x (neg.f64 x))) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (sin.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)))) (* 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 x x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)))
(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 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 eps eps) x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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)
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+.f64 eps (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 #s(literal 1/12 binary64) (.f64 (.f64 eps eps) x))) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/2 x) (* -1/6 eps))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(+ (sin eps) (* -1 x))
(-.f64 (sin.f64 eps) x)
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 eps) #s(literal -1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x #s(literal -1 binary64)) x (sin.f64 eps))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
(* -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)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (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 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* 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 #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))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin x)
(sin.f64 x)
(- (* (cos x) (sin eps)) (sin x))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
(cos x)
(cos.f64 x)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.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 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) eps (cos.f64 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 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.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 (cos.f64 x) #s(literal -1/6 binary64))) eps (.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 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* eps (cos x)) (sin x))
(fma.f64 (cos.f64 x) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(fma.f64 (cos.f64 x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) (neg.f64 (sin.f64 x)))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (fma.f64 (cos.f64 x) eps (neg.f64 (sin.f64 x))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.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 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 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)
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (/.f64 (cos.f64 x) eps) eps))) eps) eps)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)
(cos eps)
(cos.f64 eps)
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (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 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(*.f64 (neg.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) eps) eps)
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)

rewrite203.0ms (1.6%)

Memory

8.0MiB live, 234.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	193
0	65	179
1	236	179
2	2041	179
0	9917	179

Stop Event

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

Counts

22 → 595

Calls

Call 1

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

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

eval210.0ms (1.7%)

Memory: -1.8MiB live, 210.2MiB allocated
Compiler: Compiled 27 758 to 2 982 computations (89.3% saved)

prune33.0ms (0.3%)

Memory

-14.8MiB live, 62.3MiB allocated

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	730	20	750
Fresh	2	1	3
Picked	5	0	5
Done	0	1	1
Total	737	22	759

Accuracy

100.0%

Counts

759 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.0%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	98.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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))))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))
▶	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
▶	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
▶	99.8%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))

Compiler

Compiled 1 257 to 838 computations (33.3% saved)

simplify178.0ms (1.4%)

Memory

2.9MiB live, 160.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
cost-diff	0	(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
cost-diff	0	(pow.f64 eps #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
cost-diff	0	#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff	192	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff	0	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff	0	(sin.f64 x)
cost-diff	0	(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
cost-diff	0	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	507
0	100	506
1	174	504
2	311	504
3	626	504
4	1086	504
5	1742	504
6	2016	504
7	2488	504
8	3090	504
9	3742	504
10	3988	504
11	5020	504
12	7713	504
0	8260	487

Stop Event

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

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 x)
x
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
eps
#s(literal 1 binary64)
(*.f64 (cos.f64 x) (sin.f64 eps))
(cos.f64 x)
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(pow.f64 eps #s(literal 3 binary64))
eps
#s(literal 3 binary64)
(fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))
#s(literal 1/120 binary64)
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(+.f64 eps x)
eps
x
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
(cos.f64 x)

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

localize660.0ms (5.2%)

Memory

-10.9MiB live, 305.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.3515625	(*.f64 #s(literal -1/6 binary64) eps)
accuracy	0.37109375	(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
accuracy	0.5221282684660586	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
accuracy	0.9244619252693528	#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
accuracy	0.0	(*.f64 eps eps)
accuracy	0.00390625	(fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))
accuracy	0.42623732108200146	#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps))
accuracy	1.4830018777613097	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
accuracy	0.006191259768442017	(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
accuracy	0.5221282684660586	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
accuracy	0.9010263110054292	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy	0.00390625	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.7329763515270904	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	1.4966075743404244	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0.0	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
accuracy	0.0078125	(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
accuracy	0.01171875	(*.f64 (cos.f64 x) (sin.f64 eps))
accuracy	28.5021456200077	(-.f64 (cos.f64 eps) #s(literal 1 binary64))

Samples

490.0ms	169×	2	valid
84.0ms	81×	1	valid
4.0ms	1×	3	valid
2.0ms	5×	0	valid

Compiler

Compiled 822 to 122 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 501.0ms

adjust: 313.0ms (62.5% of total)

ival-mult: 59.0ms (11.8% of total)

ival-add: 42.0ms (8.4% of total)

ival-cos: 32.0ms (6.4% of total)

ival-sin: 32.0ms (6.4% of total)

const: 13.0ms (2.6% of total)

ival-sub: 5.0ms (1% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory

30.8MiB live, 30.8MiB allocated

Counts

25 → 108

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(pow.f64 eps #s(literal 3 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(*.f64 (cos.f64 x) (sin.f64 eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))
(*.f64 eps eps)
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(*.f64 #s(literal -1/6 binary64) eps)

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) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
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 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(sin x)
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* (cos x) (sin eps))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* 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))))
(pow eps 3)
(* -1/2 (sin x))
(* 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))))))))
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
-1/6
(- (* 1/120 (pow eps 2)) 1/6)
(pow eps 2)
(- (cos eps) 1)
(* -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)))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* 1/120 (pow eps 5))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 2))
(* (pow eps 2) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps))) (sin x) (- (cos eps) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (pow eps 3) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) (sin eps)) (+ (* 1/12 (* eps eps)) -1/2) (+ (* 1/120 (* eps eps)) -1/6) (* eps eps) (* (+ eps x) 1/12) (* -1/6 eps))
4.0ms	eps	@	inf	((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps))) (sin x) (- (cos eps) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (pow eps 3) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) (sin eps)) (+ (* 1/12 (* eps eps)) -1/2) (+ (* 1/120 (* eps eps)) -1/6) (* eps eps) (* (+ eps x) 1/12) (* -1/6 eps))
4.0ms	eps	@	-inf	((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps))) (sin x) (- (cos eps) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (pow eps 3) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) (sin eps)) (+ (* 1/12 (* eps eps)) -1/2) (+ (* 1/120 (* eps eps)) -1/6) (* eps eps) (* (+ eps x) 1/12) (* -1/6 eps))
4.0ms	x	@	inf	((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps))) (sin x) (- (cos eps) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (pow eps 3) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) (sin eps)) (+ (* 1/12 (* eps eps)) -1/2) (+ (* 1/120 (* eps eps)) -1/6) (* eps eps) (* (+ eps x) 1/12) (* -1/6 eps))
3.0ms	x	@	-inf	((+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps))) (sin x) (- (cos eps) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (pow eps 3) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) (sin eps)) (+ (* 1/12 (* eps eps)) -1/2) (+ (* 1/120 (* eps eps)) -1/6) (* eps eps) (* (+ eps x) 1/12) (* -1/6 eps))

simplify226.0ms (1.8%)

Memory

-22.2MiB live, 98.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	1392
1	1091	1347
2	3132	1320
0	8134	1194

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

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) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
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 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(sin x)
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* (cos x) (sin eps))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* 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))))
(pow eps 3)
(* -1/2 (sin x))
(* 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))))))))
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
-1/6
(- (* 1/120 (pow eps 2)) 1/6)
(pow eps 2)
(- (cos eps) 1)
(* -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)))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* 1/120 (pow eps 5))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 2))
(* (pow eps 2) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))

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) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 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))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
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 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 eps eps) x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
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(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
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(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+.f64 eps (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
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(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/2 x) (* -1/6 eps))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
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(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
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(* 1/12 eps)
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(+ (* 1/12 eps) (* 1/12 x))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
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(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
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(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)
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(* -1/2 (pow eps 2))
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(cos x)
(cos.f64 x)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(pow eps 3)
(pow.f64 eps #s(literal 3 binary64))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(*.f64 (cos.f64 x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(fma.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (cos.f64 x) eps))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x))) eps)
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (pow eps 2)) 1/2)
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow eps 2)) 1/6)
(fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(pow eps 2)
(*.f64 eps eps)
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(* -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)
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(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps)
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/6 binary64)) (.f64 eps eps))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 (.f64 x x) eps) x) (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/6 binary64))) (*.f64 eps eps))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
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(*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/6 binary64))
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(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps) eps)
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(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (/.f64 (cos.f64 x) eps) eps))) eps) eps)
(* 1/120 (pow eps 5))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))
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(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)
(* 1/12 (pow eps 2))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))) eps) eps)
(* 1/120 (pow eps 2))
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(* (pow eps 2) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) eps) eps)
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
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(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
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(*.f64 (neg.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64)))
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(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1/120 binary64))) (pow.f64 eps #s(literal 5 binary64)))
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(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps)

rewrite250.0ms (2%)

Memory

-9.6MiB live, 150.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	432
0	100	424
1	422	414
2	3321	414
0	8859	401

Stop Event

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

Counts

25 → 446

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(pow.f64 eps #s(literal 3 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(*.f64 (cos.f64 x) (sin.f64 eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))
(*.f64 eps eps)
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(*.f64 #s(literal -1/6 binary64) eps)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x))) (pow.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) (-.f64 (pow.f64 (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) (pow.f64 (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)) (*.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (fma.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) #s(literal -2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) #s(literal -2 binary64) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -2 binary64)))
(/.f64 (fma.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 2 binary64) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 1 binary64))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal -2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -2 binary64) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -2 binary64)))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 1 binary64))) (*.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))))
(/.f64 (fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (sin.f64 (-.f64 x eps)) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (.f64 (sin.f64 (-.f64 x eps)) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x)))) (.f64 (sin.f64 (-.f64 x eps)) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (.f64 (sin.f64 (-.f64 x eps)) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))))) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x)))) (.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (+.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal 4 binary64) (+.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 #s(literal 0 binary64) (sin.f64 x)))) (.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (.f64 #s(literal 4 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))))))
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(fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps) #s(literal 2 binary64)) (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (neg.f64 (cos.f64 x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (neg.f64 (cos.f64 x)))))
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#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
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(/.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x)))))
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(pow.f64 (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/24 binary64)))) (fma.f64 #s(literal 1/1728 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
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(/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))
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(fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
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(-.f64 (/.f64 (.f64 #s(literal 1/144 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
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(.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/36 binary64)) (pow.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/1728000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/216 binary64)) (pow.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/36 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps eps) #s(literal -1/720 binary64)))) (fma.f64 #s(literal 1/1728000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/216 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 eps eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/36 binary64))) (neg.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/1728000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/216 binary64))) (neg.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps eps) #s(literal -1/720 binary64))))))
(/.f64 (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/36 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)))
(/.f64 (fma.f64 #s(literal 1/1728000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (-.f64 (.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64))) (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(/.f64 (fma.f64 #s(literal 1/1728000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/216 binary64)) (fma.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps eps) #s(literal -1/720 binary64)))))
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(fma.f64 (*.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))
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(-.f64 (/.f64 (.f64 #s(literal 1/14400 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))))
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(*.f64 eps eps)
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(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(*.f64 (+.f64 eps x) #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) (+.f64 eps x))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) #s(literal 1/12 binary64)) (-.f64 eps x))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) #s(literal 1/12 binary64)) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/12 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/12 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 #s(literal 1/12 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps eps (.f64 x (-.f64 x eps))))
(/.f64 (.f64 #s(literal 1/12 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(fma.f64 #s(literal 1/12 binary64) eps (*.f64 #s(literal 1/12 binary64) x))
(fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/12 binary64) eps))
(fma.f64 eps #s(literal 1/12 binary64) (*.f64 #s(literal 1/12 binary64) x))
(fma.f64 x #s(literal 1/12 binary64) (*.f64 #s(literal 1/12 binary64) eps))
(+.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 #s(literal 1/12 binary64) eps))
(+.f64 (.f64 #s(literal 1/12 binary64) eps) (.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 eps #s(literal -1/6 binary64))

eval91.0ms (0.7%)

Memory: 45.7MiB live, 117.1MiB allocated
Compiler: Compiled 31 466 to 2 770 computations (91.2% saved)

prune75.0ms (0.6%)

Memory

-30.1MiB live, 56.2MiB allocated

Pruning

29 alts after pruning (24 fresh and 5 done)

	Pruned	Kept	Total
New	538	12	550
Fresh	4	12	16
Picked	1	4	5
Done	0	1	1
Total	543	29	572

Accuracy

100.0%

Counts

572 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	98.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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))))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
	46.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
	48.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (.f64 x x)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
✓	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
▶	5.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
✓	99.8%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
	99.5%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (.f64 (cos.f64 x) (sin.f64 eps))))
	99.4%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))

Compiler

Compiled 2 087 to 1 357 computations (35% saved)

simplify303.0ms (2.4%)

Memory

0.1MiB live, 148.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
cost-diff	0	(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
cost-diff	0	(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
cost-diff	0	#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
cost-diff	0	#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
cost-diff	0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	822
0	128	816
1	220	816
2	533	816
3	1468	816
4	2244	816
5	2877	816
6	3063	816
7	3428	816
8	3447	816
9	3730	812
10	4162	812
11	4315	812
12	4505	812
13	5666	812
0	8079	772

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
eps
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
(pow.f64 eps #s(literal 5 binary64))
eps
#s(literal 5 binary64)
#s(literal 1/120 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(fma.f64 #s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64))
#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
(cos.f64 x)

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(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)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
eps
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
(pow.f64 eps #s(literal 5 binary64))
eps
#s(literal 5 binary64)
#s(literal 1/120 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(fma.f64 #s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64))
#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
(cos.f64 x)

localize330.0ms (2.6%)

Memory

13.6MiB live, 369.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3515625	(*.f64 #s(literal -1/6 binary64) eps)
accuracy	0.5221282684660586	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
accuracy	0.9244619252693528	#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
accuracy	26.56458196279672	#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
accuracy	0.04296875	(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
accuracy	0.42623732108200146	#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
accuracy	1.4830018777613097	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
accuracy	60.27764939445845	#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
accuracy	0.5221282684660586	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
accuracy	0.7726892409905262	#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
accuracy	0.9010263110054292	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
accuracy	0.5221282684660586	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
accuracy	0.9010263110054292	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
accuracy	0.9162390470528912	#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.0571568094868315	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.2667512751702433	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))

Samples

189.0ms	85×	1	valid
81.0ms	170×	0	valid
4.0ms	1×	3	valid

Compiler

Compiled 1 257 to 169 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 228.0ms

ival-mult: 79.0ms (34.7% of total)

const: 61.0ms (26.8% of total)

adjust: 37.0ms (16.2% of total)

ival-add: 26.0ms (11.4% of total)

ival-sin: 10.0ms (4.4% of total)

ival-pow: 6.0ms (2.6% of total)

ival-cos: 4.0ms (1.8% of total)

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

ival-sub: 1.0ms (0.4% of total)

exact: 1.0ms (0.4% of total)

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

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

series21.0ms (0.2%)

Memory

-3.5MiB live, 33.6MiB allocated

Counts

24 → 108

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal -1/6 binary64) eps)

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(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 (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(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))))))
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* 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
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* 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))))
(* 1/120 (pow eps 5))
(* -1/2 (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (* (pow eps 5) 1/120) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/12 (* eps eps)) -1/2) (* (+ eps x) 1/12) (* -1/6 eps))
3.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (* (pow eps 5) 1/120) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/12 (* eps eps)) -1/2) (* (+ eps x) 1/12) (* -1/6 eps))
2.0ms	eps	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (* (pow eps 5) 1/120) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/12 (* eps eps)) -1/2) (* (+ eps x) 1/12) (* -1/6 eps))
2.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (* (pow eps 5) 1/120) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/12 (* eps eps)) -1/2) (* (+ eps x) 1/12) (* -1/6 eps))
2.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (sin eps) (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (* (pow eps 5) 1/120) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/12 (* eps eps)) -1/2) (* (+ eps x) 1/12) (* -1/6 eps))

simplify189.0ms (1.5%)

Memory

25.7MiB live, 227.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	422	1544
1	1250	1475
2	3533	1434
0	8385	1316

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

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))))))))))
(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 (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(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))))))
(* 1/12 eps)
(+ (* 1/12 eps) (* 1/12 x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 1/12 x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(* 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
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* 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))))
(* 1/120 (pow eps 5))
(* -1/2 (sin x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
-1/2
(- (* 1/12 (pow eps 2)) 1/2)
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 1/12 (pow eps 2))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (.f64 x (neg.f64 x))) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 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 x x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (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)))
(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 (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+.f64 eps (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) eps (.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) x)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/2 x) (* -1/6 eps))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64)) x (.f64 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* 1/12 eps)
(*.f64 #s(literal 1/12 binary64) eps)
(+ (* 1/12 eps) (* 1/12 x))
(*.f64 (+.f64 x eps) #s(literal 1/12 binary64))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* 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 #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))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (*.f64 x x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* x (+ 1/12 (* 1/12 (/ eps x))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (neg.f64 x))) x)) (.f64 x x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(* -1 (* x (- (* -1/12 (/ eps x)) 1/12)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) x)
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (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 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.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
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 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 (fma.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 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* 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)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps (.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ 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 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* 1/120 (pow eps 5))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (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 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) eps (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (pow eps 2)) 1/2)
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* -1/645120 (pow eps 7))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64)))) #s(literal 1/645120 binary64)) (pow.f64 eps #s(literal 7 binary64)))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 eps eps))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps)
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/6 binary64)) (.f64 eps eps))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 (.f64 x x) eps) x) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/6 binary64))) (*.f64 eps eps))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (+.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 5 binary64)))
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))) eps) eps)
(* eps (+ 1/12 (* 1/12 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps)
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (pow.f64 eps #s(literal 7 binary64)))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 7 binary64)))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 7 binary64))) (-.f64 (+.f64 (-.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (cos.f64 x)) #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 5 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(* -1 (* eps (- (* -1/12 (/ x eps)) 1/12)))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps)

rewrite231.0ms (1.8%)

Memory

-30.2MiB live, 254.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	679
0	128	673
1	503	673
2	4273	673
0	10713	634

Stop Event

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

Counts

24 → 270

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))))
#s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal -1/6 binary64) eps)

Outputs
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 eps (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (neg.f64 eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (.f64 (neg.f64 eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 eps eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64))))))
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(fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps) #s(literal 2 binary64)) (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (neg.f64 (cos.f64 x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (neg.f64 (cos.f64 x)))))
(+.f64 (.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
#s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64))
#s(approx (* (+ eps x) 1/12) (*.f64 #s(literal 1/12 binary64) x))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 eps #s(literal -1/6 binary64))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/6 binary64)) (neg.f64 eps))
(/.f64 (.f64 #s(literal -1/6 binary64) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (.f64 eps eps))
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/6 binary64) eps))

eval94.0ms (0.7%)

Memory: -9.6MiB live, 74.4MiB allocated
Compiler: Compiled 24 946 to 1 814 computations (92.7% saved)

prune31.0ms (0.2%)

Memory

25.5MiB live, 63.4MiB allocated

Pruning

29 alts after pruning (21 fresh and 8 done)

	Pruned	Kept	Total
New	354	8	362
Fresh	6	13	19
Picked	2	3	5
Done	0	5	5
Total	362	29	391

Accuracy

100.0%

Counts

391 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	52.1%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	98.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
	46.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
✓	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	5.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
✓	99.8%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
	99.5%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (.f64 (cos.f64 x) (sin.f64 eps))))
	99.4%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))

Compiler

Compiled 2 905 to 1 100 computations (62.1% saved)

regimes44.0ms (0.3%)

Memory

-17.7MiB live, 63.5MiB allocated

Counts

49 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) #s(approx (- (cos eps) 1) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)) (.f64 (cos.f64 x) (sin.f64 eps))))
#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (sin.f64 x))) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))))

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

Calls

3 calls:

15.0ms	x
14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.3%)

Memory

16.2MiB live, 55.1MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))

Outputs

(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))

Calls

3 calls:

11.0ms	eps
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes59.0ms (0.5%)

Memory

1.8MiB live, 40.4MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Calls

3 calls:

40.0ms	eps
9.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.3%)

Memory

4.1MiB live, 43.2MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

21.0ms	eps
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.2%)

Memory

0.2MiB live, 42.2MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.2%)

Memory

-9.0MiB live, 65.1MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 #s(approx (* (+ eps x) 1/12) (.f64 #s(literal 1/12 binary64) x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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))))

Calls

3 calls:

11.0ms	x
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.2%)

Memory

21.9MiB live, 61.1MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

8.0ms	eps
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes48.0ms (0.4%)

Memory

-24.1MiB live, 68.6MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (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) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)))

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

Calls

3 calls:

32.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

5.3MiB live, 42.1MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) (/.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)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps)) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (+.f64 (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (/.f64 #s(literal -1/6 binary64) x) x) #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #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)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/120 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

-14.0MiB live, 24.0MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1/2 binary64)) (.f64 x x)))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-21.2MiB live, 20.9MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* (pow eps 3) (+ (* 1/120 (* eps eps)) -1/6)) eps) (.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps)) eps eps)))

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

Calls

3 calls:

7.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

11.1MiB live, 11.1MiB allocated

Accuracy

Total -0.1b remaining (-3.7%)

Threshold costs -0.1b (-3.7%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`eps`
97.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify29.0ms (0.2%)

Memory

-25.5MiB live, 51.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	485
1	173	485
2	177	485
3	179	485
4	180	485

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

Outputs
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))))
(.f64 #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) x))) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (.f64 (+.f64 x eps) x) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/12 (* eps eps)) -1/2) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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) -1/2) eps) (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)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 x eps) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

soundness1.4s (11.2%)

Memory

34.0MiB live, 852.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	314	291
2	779	284
3	2842	284
4	6177	284
0	8125	253
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	422	1544
1	1250	1475
2	3533	1434
0	8385	1316
0	438	1583
1	1321	1512
2	3644	1476
0	8196	1329
0	360	1392
1	1091	1347
2	3132	1320
0	8134	1194

Stop Event

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

Compiler

Compiled 808 to 395 computations (51.1% saved)

preprocess108.0ms (0.8%)

Memory: 3.0MiB live, 158.3MiB allocated
Compiler: Compiled 1 014 to 318 computations (68.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze47.0ms (0.4%)

sample6.3s (49.4%)

explain89.0ms (0.7%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize24.0ms (0.2%)

series4.0ms (0%)

simplify165.0ms (1.3%)

rewrite172.0ms (1.4%)

eval29.0ms (0.2%)

prune8.0ms (0.1%)

simplify325.0ms (2.6%)

localize190.0ms (1.5%)

series43.0ms (0.3%)

simplify225.0ms (1.8%)

rewrite203.0ms (1.6%)

eval210.0ms (1.7%)

prune33.0ms (0.3%)

simplify178.0ms (1.4%)

localize660.0ms (5.2%)

series27.0ms (0.2%)

simplify226.0ms (1.8%)

rewrite250.0ms (2%)

eval91.0ms (0.7%)

prune75.0ms (0.6%)

simplify303.0ms (2.4%)

localize330.0ms (2.6%)

series21.0ms (0.2%)

simplify189.0ms (1.5%)

rewrite231.0ms (1.8%)

eval94.0ms (0.7%)

prune31.0ms (0.2%)

regimes44.0ms (0.3%)

regimes33.0ms (0.3%)

regimes59.0ms (0.5%)

regimes40.0ms (0.3%)

regimes30.0ms (0.2%)

regimes31.0ms (0.2%)

regimes24.0ms (0.2%)

regimes48.0ms (0.4%)

regimes22.0ms (0.2%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes14.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify29.0ms (0.2%)

soundness1.4s (11.2%)

preprocess108.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18