Metrics for 2sin (example 3.3)

analyze39.0ms (0.3%)

Memory

24.5MiB live, 62.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.4s (44.2%)

Memory

-19.3MiB live, 8 482.0MiB allocated

Samples

3.6s	25 541×	0	invalid
653.0ms	5 406×	0	valid
476.0ms	2 850×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-sin: 882.0ms (25.1% of total)

const: 809.0ms (23% of total)

ival-add: 328.0ms (9.3% of total)

ival-<=: 288.0ms (8.2% of total)

ival-mult: 265.0ms (7.5% of total)

ival-fabs: 252.0ms (7.2% of total)

ival-sub: 251.0ms (7.1% of total)

ival-<: 207.0ms (5.9% of total)

ival-and: 99.0ms (2.8% of total)

adjust: 71.0ms (2% of total)

exact: 45.0ms (1.3% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

preprocess28.0ms (0.2%)

Memory

-8.9MiB live, 35.6MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

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))

explain93.0ms (0.6%)

Memory

-7.3MiB live, 70.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
221	1	(-5.670654569479482e-178 5.008009389092732e-181)	2	(3.225780371294668e-135 3.531463027326352e-137)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	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	220	7
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	221	2
-	1	32

Precision

0.9954954954954955

Recall

0.9910313901345291

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	221	2	0
-	1	5	27

Precision?

0.9737991266375546

Recall?

1.0

Freqs

test

number	freq
0	34
1	222

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	354×	0	valid
15.0ms	154×	1	valid
1.0ms	2×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 9.0ms (48% of total)

adjust: 3.0ms (16% of total)

ival-add: 3.0ms (16% of total)

ival-sub: 3.0ms (16% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

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

localize23.0ms (0.2%)

Memory

19.9MiB live, 19.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

8.0ms	177×	0	valid
7.0ms	77×	1	valid
0.0ms	1×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sin: 4.0ms (43.7% of total)

ival-add: 2.0ms (21.9% of total)

adjust: 1.0ms (10.9% of total)

ival-sub: 1.0ms (10.9% of total)

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

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

series3.0ms (0%)

Memory

3.3MiB live, 3.2MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (sin.f64 x)>

Outputs
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>

Calls

21 calls:

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

simplify508.0ms (3.5%)

Memory

-2.2MiB live, 279.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

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

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

rewrite454.0ms (3.1%)

Memory

6.5MiB live, 237.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 986×	`lower-fma.f64`
4 986×	`lower-fma.f32`
4 676×	`lower-*.f64`
4 676×	`lower-*.f32`
2 176×	`lower-/.f64`

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

eval201.0ms (1.4%)

Memory: -33.8MiB live, 48.2MiB allocated
Compiler: Compiled 7 746 to 844 computations (89.1% saved)

prune39.0ms (0.3%)

Memory

29.2MiB live, 104.4MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	281	10	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	281	11	292

Accuracy

100.0%

Counts

292 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
▶	7.8%	(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
▶	63.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
	63.7%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.9%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 319 to 208 computations (34.8% saved)

simplify353.0ms (2.4%)

Memory

-4.3MiB live, 515.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
✓	cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
✓	cost-diff	192	(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))
✓	cost-diff	256	(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	cost-diff	0	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

14 160×	`lower-fma.f32`
14 150×	`lower-fma.f64`
3 734×	`lower-*.f32`
3 716×	`lower-*.f64`
2 982×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	341
0	86	319
1	143	319
2	288	313
3	627	305
4	1532	304
5	5015	304
6	7737	304
0	8529	298

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(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
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
(*.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 x x))
(+.f64 x x)
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 x)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 eps (+.f64 x x))
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(-.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)
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
(.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 (+.f64 x eps) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 x x))
(+.f64 x x)
(+.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))
(sin.f64 x)

localize393.0ms (2.7%)

Memory

-13.9MiB live, 635.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	accuracy	55.7%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
✓	accuracy	55.1%	(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	accuracy	53.9%	(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
✓	accuracy	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
✓	accuracy	98.1%	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
✓	accuracy	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

183.0ms	141×	2	valid
71.0ms	37×	3	valid
51.0ms	71×	1	valid
3.0ms	7×	0	valid

Compiler

Compiled 317 to 48 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 258.0ms

ival-cos: 95.0ms (36.8% of total)

ival-mult: 47.0ms (18.2% of total)

adjust: 45.0ms (17.5% of total)

ival-add: 21.0ms (8.1% of total)

ival-div: 15.0ms (5.8% of total)

const: 15.0ms (5.8% of total)

ival-sin: 12.0ms (4.7% of total)

ival-sub: 5.0ms (1.9% of total)

exact: 1.0ms (0.4% of total)

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

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

series37.0ms (0.3%)

Memory

20.9MiB live, 59.1MiB allocated

Counts

21 → 432

Calls

Call 1

Inputs
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))>
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>
#<alt (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))>
#<alt (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))>
#<alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))>
#<alt (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))>
#<alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))>
#<alt (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))>

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
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#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
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#<alt (sin eps)>
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#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
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#<alt eps>
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#<alt x>
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#<alt eps>
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#<alt (sin x)>
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#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))>
#<alt (+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))))>
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#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))>
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))>
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#<alt (pow x 2)>
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#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))>
#<alt (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps)))>
#<alt (+ (* -1 (* x (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))) (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))))>
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (* x (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))) (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))))))>
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (* x (+ (* -1 (* x (- (* 2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- (* -1/6 (cos eps)) 1/6) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) (* -1 (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))>
#<alt (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))>
#<alt (+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))))>
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))))))>
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/120 x)>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (+ 1 (cos eps))))>
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))>
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (+ (sin x) (sin (- eps (* -1 x))))>
#<alt (* 2 (sin x))>
#<alt (+ (* 2 (sin x)) (* eps (cos x)))>
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (+ eps x)))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>
#<alt (+ (sin x) (sin (- x (* -1 eps))))>

Calls

108 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x))))))
3.0ms	eps	@	inf	(- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x))))))
2.0ms	eps	@	-inf	(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x)))
1.0ms	eps	@	0	(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x)))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

simplify374.0ms (2.6%)

Memory

5.1MiB live, 442.3MiB allocated

Algorithm

1×	egg-herbie

Rules

10 708×	`lower-fma.f64`
10 708×	`lower-fma.f32`
5 268×	`lower-*.f64`
5 268×	`lower-*.f32`
4 806×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	590	5491
1	1815	5145
2	5276	4941
0	8688	4623

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 409

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin 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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(/ 1 (sin eps))
(+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (* eps (cos x)))
(/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- 1/2 (* 1/2 (cos (* 2 eps))))
(- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))
(- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))
(- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))
(- (* eps (sin (* 2 x))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))
(- (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))
(- (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(* 1/2 (cos (* 2 eps)))
(+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))
(+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps))))))))
(+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))
(+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x)))))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps)))
(+ (* -1 (* x (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))) (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))))
(+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (* x (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))) (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))))))
(+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (* x (+ (* -1 (* x (- (* 2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- (* -1/6 (cos eps)) 1/6) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) (* -1 (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))))))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))
(+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))))
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))))))
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))))))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(sin eps)
(+ (sin eps) (* x (+ 1 (cos eps))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (- eps (* -1 x))))
(+ (sin x) (sin (- eps (* -1 x))))
(+ (sin x) (sin (- eps (* -1 x))))
(+ (sin x) (sin (- eps (* -1 x))))
(* 2 (sin x))
(+ (* 2 (sin x)) (* eps (cos x)))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (+ eps x)))
(+ (sin x) (sin (- x (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))
(+ (sin x) (sin (- x (* -1 eps))))

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

rewrite141.0ms (1%)

Memory

-13.8MiB live, 141.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 216×	`lower-*.f32`
1 200×	`lower-*.f64`
1 192×	`lower-fma.f32`
1 184×	`lower-fma.f64`
954×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	228
0	86	233
1	326	182
0	2761	177

Stop Event

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

Counts

21 → 547

Calls

Call 1

Inputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

eval139.0ms (1%)

Memory: 0.7MiB live, 185.1MiB allocated
Compiler: Compiled 28 575 to 2 252 computations (92.1% saved)

prune109.0ms (0.8%)

Memory

-13.8MiB live, 162.7MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	1 136	15	1 151
Fresh	4	1	5
Picked	4	1	5
Done	0	1	1
Total	1 144	18	1 162

Accuracy

100.0%

Counts

1 162 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	7.8%	(/.f64 #s(approx (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
✓	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	25.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	21.1%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	63.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	53.0%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	5.5%	#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
	98.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)))))
	98.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 649 to 405 computations (37.6% saved)

simplify284.0ms (2%)

Memory

42.8MiB live, 312.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(fma.f64 x x (*.f64 (+.f64 x eps) x))
✓	cost-diff	256	(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	5440	(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	384	(+.f64 x (-.f64 eps x))
✓	cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	0	#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Rules

12 636×	`lower-fma.f32`
12 626×	`lower-fma.f64`
3 426×	`lower-*.f32`
3 394×	`lower-*.f64`
3 312×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	533
0	102	476
1	183	469
2	414	455
3	1024	435
4	2797	429
5	6965	429
0	8081	423

Stop Event

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

Calls

Call 1

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

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

localize429.0ms (3%)

Memory

-0.7MiB live, 481.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))
✓	accuracy	99.6%	(pow.f64 (+.f64 x eps) #s(literal 3 binary64))
✓	accuracy	89.1%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x)))
✓	accuracy	33.7%	(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	63.7%	(+.f64 x (-.f64 eps x))
✓	accuracy	100.0%	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/48 binary64))
✓	accuracy	98.9%	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	5.5%	#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.9%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

190.0ms	141×	2	valid
70.0ms	71×	1	valid
68.0ms	37×	3	valid
4.0ms	7×	0	valid

Compiler

Compiled 519 to 61 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 278.0ms

ival-cos: 99.0ms (35.6% of total)

adjust: 57.0ms (20.5% of total)

ival-mult: 49.0ms (17.6% of total)

ival-sin: 23.0ms (8.3% of total)

ival-add: 22.0ms (7.9% of total)

ival-pow: 8.0ms (2.9% of total)

ival-div: 7.0ms (2.5% of total)

ival-sub: 6.0ms (2.2% of total)

const: 4.0ms (1.4% of total)

exact: 1.0ms (0.4% of total)

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

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

series38.0ms (0.3%)

Memory

-22.8MiB live, 14.5MiB allocated

Counts

21 → 468

Calls

Call 1

Inputs
#<alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))>
#<alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))>
#<alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))>
#<alt #s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))>
#<alt (+.f64 x (-.f64 eps x))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt (pow.f64 (+.f64 x eps) #s(literal 3 binary64))>
#<alt (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))>
#<alt (fma.f64 x x (*.f64 (+.f64 x eps) x))>
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (*.f64 eps #s(literal -1/48 binary64))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))>
#<alt (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))>
#<alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x)))>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
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#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x))))>
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))))>
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3))))))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1)))>
#<alt (pow x 3)>
#<alt (+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3))>
#<alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3))>
#<alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3))>
#<alt (pow eps 3)>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))))>
#<alt (pow eps 3)>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1)))>
#<alt (pow eps 2)>
#<alt (+ (* x (+ eps (* 2 eps))) (pow eps 2))>
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))>
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))>
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))>
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))>
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))>
#<alt (+ (* 2 (pow x 2)) (pow x 2))>
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))>
#<alt (* eps x)>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* x (+ eps (* 2 x)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* (pow x 2) (+ 2 (/ eps x)))>
#<alt (* 2 (pow x 2))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (+ (* 2 (pow x 2)) (* eps x))>
#<alt (* eps x)>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))>
#<alt (* eps x)>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))>
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 1/3 (+ eps (* 2 eps)))>
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))>
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))>
#<alt (- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))>
#<alt (* 1/3 (+ eps (* 2 eps)))>
#<alt (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))>
#<alt (pow eps 3)>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))>
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))>
#<alt (* (pow x 2) (+ eps (* 2 eps)))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))>
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))>
#<alt (* (pow x 2) (+ eps (* 2 eps)))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))>
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))>
#<alt (* eps (+ (* 2 (pow x 2)) (pow x 2)))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))>
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))>
#<alt (pow eps 3)>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))>
#<alt (pow eps 3)>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))>

Calls

117 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	(pow (+ x eps) 3)
6.0ms	x	@	-inf	(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))
2.0ms	eps	@	0	(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))
1.0ms	x	@	0	(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))
1.0ms	eps	@	inf	(/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x))))

simplify397.0ms (2.8%)

Memory

19.1MiB live, 546.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 388×	`lower-fma.f64`
11 388×	`lower-fma.f32`
5 430×	`lower-*.f64`
5 430×	`lower-*.f32`
4 328×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	630	6892
1	2048	6206
2	7282	6173
0	8166	5757

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 428

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
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(pow eps 3)
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1)))
(pow eps 2)
(+ (* x (+ eps (* 2 eps))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))
(+ (* 2 (pow x 2)) (pow x 2))
(+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))
(* eps x)
(* x (+ eps (* 2 x)))
(* x (+ eps (* 2 x)))
(* x (+ eps (* 2 x)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* (pow x 2) (+ 2 (/ eps x)))
(* 2 (pow x 2))
(+ (* 2 (pow x 2)) (* eps x))
(+ (* 2 (pow x 2)) (* eps x))
(+ (* 2 (pow x 2)) (* eps x))
(* eps x)
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps (+ x (* 2 (/ (pow x 2) eps))))
(* eps x)
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
eps
eps
eps
eps
(* 1/3 (+ eps (* 2 eps)))
(- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))
(- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(* 1/3 (+ eps (* 2 eps)))
(+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(pow eps 3)
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(* (pow x 2) (+ eps (* 2 eps)))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(* (pow x 2) (+ eps (* 2 eps)))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(* eps (+ (* 2 (pow x 2)) (pow x 2)))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(pow eps 3)
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(pow eps 3)
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) (.f64 x (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64)) (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
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(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
eps
eps
eps
eps
(* 1/3 (+ eps (* 2 eps)))
eps
(- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))
(+.f64 eps (/.f64 (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) #s(literal -1/9 binary64) (*.f64 eps eps)) x))
(- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(-.f64 (fma.f64 eps (/.f64 eps x) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/3 binary64) (.f64 x x)) eps)) (fma.f64 eps (/.f64 (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) #s(literal -1/9 binary64) (.f64 eps eps)) (.f64 x x)) (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/9 binary64) x) (/.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (*.f64 x x)))))
(- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))
(-.f64 (-.f64 (fma.f64 eps (/.f64 eps x) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/3 binary64) (.f64 x x)) eps)) (fma.f64 eps (/.f64 (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) #s(literal -1/9 binary64) (.f64 eps eps)) (.f64 x x)) (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) (/.f64 #s(literal 1/9 binary64) x) (/.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (.f64 x x))))) (/.f64 (fma.f64 eps (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (fma.f64 eps (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) #s(literal -1/9 binary64) (.f64 eps eps)) (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))))) (.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (fma.f64 (.f64 #s(literal 9 binary64) (.f64 eps eps)) #s(literal -1/9 binary64) (.f64 eps eps))))) (.f64 x (.f64 x x))))
(* 1/3 (+ eps (* 2 eps)))
eps
(+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(-.f64 eps (/.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) x))
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(-.f64 eps (/.f64 (-.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) (/.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) (.f64 #s(literal 1/3 binary64) (.f64 eps #s(literal -3 binary64)))))) x)) x))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))
(-.f64 eps (/.f64 (-.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) (/.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (.f64 eps #s(literal -3 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) (.f64 #s(literal 1/3 binary64) (.f64 eps #s(literal -3 binary64)))))) x) (.f64 (.f64 eps eps) (+.f64 (/.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) x) eps)))) (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (.f64 (-.f64 (.f64 eps (neg.f64 eps)) (.f64 eps (neg.f64 eps))) (.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64)))))) x)) x))
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal 3 binary64) (*.f64 x #s(literal -3 binary64))) eps) eps)
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal -3 binary64) (fma.f64 x #s(literal 3 binary64) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal -3 binary64)) (fma.f64 x (.f64 #s(literal -3 binary64) (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64)))) (.f64 (.f64 x x) #s(literal -3 binary64)))) (neg.f64 eps)))) (neg.f64 eps)) eps)
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal -3 binary64) (-.f64 (.f64 x #s(literal 3 binary64)) (/.f64 (-.f64 (fma.f64 x (.f64 x #s(literal -3 binary64)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal -3 binary64)) (fma.f64 x (.f64 #s(literal -3 binary64) (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64)))) (.f64 (.f64 x x) #s(literal -3 binary64)))) (/.f64 (.f64 x #s(literal -3 binary64)) eps) (.f64 (.f64 x (.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64))) eps)))) (fma.f64 x (.f64 #s(literal -3 binary64) (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64)))) (.f64 (*.f64 x x) #s(literal -3 binary64)))) eps))) (neg.f64 eps)) eps)
(pow eps 3)
(.f64 eps (.f64 eps eps))
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))
(fma.f64 x (.f64 (.f64 eps eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(fma.f64 x (fma.f64 eps (.f64 x #s(literal 3 binary64)) (.f64 (.f64 eps eps) #s(literal 3 binary64))) (.f64 eps (*.f64 eps eps)))
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))
(fma.f64 x (fma.f64 eps (.f64 x #s(literal 3 binary64)) (.f64 (.f64 eps eps) #s(literal 3 binary64))) (.f64 eps (*.f64 eps eps)))
(* (pow x 2) (+ eps (* 2 eps)))
(.f64 eps (.f64 x (*.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))
(.f64 (.f64 x x) (*.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps)))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (.f64 eps (.f64 eps eps)) (*.f64 x x))))
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (.f64 eps (.f64 eps eps)) (*.f64 x x))))
(* (pow x 2) (+ eps (* 2 eps)))
(.f64 eps (.f64 x (*.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))
(.f64 x (.f64 x (-.f64 (.f64 eps #s(literal 3 binary64)) (/.f64 (.f64 eps (*.f64 eps #s(literal -3 binary64))) x))))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 3 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal -3 binary64))) (/.f64 (.f64 eps (*.f64 eps eps)) x)) x)))
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))
(.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 3 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal -3 binary64))) (/.f64 (.f64 eps (*.f64 eps eps)) x)) x)))
(* eps (+ (* 2 (pow x 2)) (pow x 2)))
(.f64 eps (.f64 x (*.f64 x #s(literal 3 binary64))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))
(.f64 eps (.f64 x (*.f64 #s(literal 3 binary64) (+.f64 eps x))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(.f64 eps (fma.f64 eps (fma.f64 x #s(literal 3 binary64) eps) (.f64 x (*.f64 x #s(literal 3 binary64)))))
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))
(.f64 eps (fma.f64 eps (fma.f64 x #s(literal 3 binary64) eps) (.f64 x (*.f64 x #s(literal 3 binary64)))))
(pow eps 3)
(.f64 eps (.f64 eps eps))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))
(.f64 (.f64 eps eps) (*.f64 eps (fma.f64 (/.f64 x eps) #s(literal 3 binary64) #s(literal 1 binary64))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))))
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))))
(pow eps 3)
(.f64 eps (.f64 eps eps))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))
(.f64 (fma.f64 x (/.f64 #s(literal -3 binary64) eps) #s(literal -1 binary64)) (.f64 (*.f64 eps (neg.f64 eps)) eps))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal 3 binary64) (/.f64 (.f64 (*.f64 x (neg.f64 x)) #s(literal -3 binary64)) eps)) eps))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))
(neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal 3 binary64) (/.f64 (.f64 (*.f64 x (neg.f64 x)) #s(literal -3 binary64)) eps)) eps))))

rewrite184.0ms (1.3%)

Memory

5.9MiB live, 309.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 136×	`lower-fma.f32`
2 128×	`lower-fma.f64`
1 702×	`lower-*.f32`
1 676×	`lower-*.f64`
1 348×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	292
0	94	247
1	390	193
0	3672	191

Stop Event

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

Counts

21 → 448

Calls

Call 1

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

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

eval136.0ms (0.9%)

Memory: 0.1MiB live, 325.8MiB allocated
Compiler: Compiled 32 896 to 2 859 computations (91.3% saved)

prune124.0ms (0.9%)

Memory

-1.2MiB live, 159.7MiB allocated

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	1 018	10	1 028
Fresh	4	7	11
Picked	3	2	5
Done	0	2	2
Total	1 025	21	1 046

Accuracy

100.0%

Counts

1 046 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
▶	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
✓	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	25.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	21.1%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (+.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (+.f64 eps x))) (.f64 x x))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	35.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (.f64 x x)) (-.f64 (-.f64 eps x) x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	15.8%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (-.f64 x (+.f64 eps x)))) eps) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 eps x)) eps)) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 eps x)) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (-.f64 x (+.f64 eps x)))) eps))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	35.5%	(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	63.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	53.0%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	73.6%	(.f64 (.f64 (sin.f64 (.f64 #s(approx (/ (- (pow (+ x eps) 3) ( x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x)))) (fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64))) eps) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
✓	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	98.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	98.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	5.5%	#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
	98.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)))))
	98.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 904 to 502 computations (44.5% saved)

simplify317.0ms (2.2%)

Memory

-16.6MiB live, 427.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	1600	(-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x))))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
✓	cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
✓	cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
✓	cost-diff	0	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))

Rules

14 596×	`lower-fma.f32`
14 580×	`lower-fma.f64`
3 804×	`lower-*.f32`
3 776×	`lower-*.f64`
1 868×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	557
0	112	545
1	192	545
2	449	532
3	1059	532
4	2201	508
5	4487	482
0	8166	474

Stop Event

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

Calls

Call 1

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

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

localize426.0ms (3%)

Memory

26.7MiB live, 257.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(-.f64 x (-.f64 eps x))
✓	accuracy	64.6%	(-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x))))
✓	accuracy	54.6%	(/.f64 (*.f64 x x) (-.f64 x (-.f64 eps x)))
✓	accuracy	54.4%	(/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
✓	accuracy	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
✓	accuracy	100.0%	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.9%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	99.4%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
✓	accuracy	98.9%	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
✓	accuracy	99.7%	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
✓	accuracy	98.8%	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
✓	accuracy	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	accuracy	71.9%	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))

Samples

285.0ms	230×	1	valid
21.0ms	17×	2	valid
5.0ms	9×	0	valid

Compiler

Compiled 449 to 66 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 268.0ms

adjust: 83.0ms (31% of total)

ival-sin: 74.0ms (27.6% of total)

ival-mult: 50.0ms (18.7% of total)

ival-add: 16.0ms (6% of total)

ival-div: 13.0ms (4.9% of total)

const: 13.0ms (4.9% of total)

ival-cos: 11.0ms (4.1% of total)

ival-sub: 6.0ms (2.2% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series71.0ms (0.5%)

Memory

-0.2MiB live, 42.5MiB allocated

Counts

26 → 528

Calls

Call 1

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

Outputs
#<alt (* x (- (cos eps) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (cos x))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
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#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (+ (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2))))>
#<alt (+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (+ (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (+ (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/4 (* (sin (* 1/2 eps)) (* (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3)))))) (* (cos (* 1/2 eps)) (+ (* -1/48 (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 3)) (* 1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/32 (pow eps 4)))))))) (pow x 3)) (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2)))))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))>
#<alt (+ (* 1/2 (/ (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2))))) x)) (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/4 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3)))))) (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (+ (* -1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* -1/32 (pow eps 4)))) (* 1/48 (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 3)))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2)))))) x)) (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* -1/48 eps)>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* 1/3840 (pow eps 3))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (* 1/2 x)>
#<alt (+ (* -3/4 eps) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (- (* 1/8 (/ eps x)) 3/4)))>
#<alt (+ (* 1/2 x) (* eps (- (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))) 3/4)))>
#<alt (* -1 eps)>
#<alt (* eps (- (* -1 (/ (pow x 2) (pow eps 2))) 1))>
#<alt (* eps (- (+ (* -2 (/ (pow x 3) (pow eps 3))) (* -1 (/ (pow x 2) (pow eps 2)))) 1))>
#<alt (* eps (- (+ (* -4 (/ (pow x 4) (pow eps 4))) (* -1 (/ (pow x 2) (pow eps 2)))) (+ 1 (* 2 (/ (pow x 3) (pow eps 3))))))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (/ (pow x 2) (pow eps 2)))))>
#<alt (* -1 (* eps (+ 1 (+ (* 2 (/ (pow x 3) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))>
#<alt (* -1 (* eps (+ 1 (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (* -1 (/ (pow x 2) eps)))>
#<alt (+ (* -1 eps) (* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps))))>
#<alt (+ (* -1 eps) (* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))))>
#<alt (* 1/2 x)>
#<alt (* x (- (+ 1/2 (* -1 (/ eps x))) (* -1/4 (/ eps x))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ eps x)) (* 1/2 (/ (pow eps 2) (pow x 2))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ eps x)) (+ (* 1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 3))) (* 1/2 (/ (pow eps 2) (pow x 2)))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (/ eps x) (+ 1/2 (* 1/4 (/ eps x))))))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ (* -1 (- eps (* 1/4 eps))) (* 1/2 (/ (pow eps 2) x))) (* 1/2 (/ (* eps (- eps (* 1/4 eps))) x))) x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1 (- eps (* 1/4 eps))) (* -1 (/ (+ (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) x))) x))) x)) 1/2)))>
#<alt (* -1 (/ (pow x 2) eps))>
#<alt (* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps)))>
#<alt (* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))>
#<alt (* (pow x 2) (- (* x (- (* x (- (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/4 (/ eps x))))>
#<alt (* x (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* -1/4 (/ eps x))))>
#<alt (* x (- (+ 1/2 (* 1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/4 (/ eps x)) (* -1/8 (/ (pow eps 2) (pow x 2))))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* -1/4 eps)) x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* -1/4 eps)) x)) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/4 eps) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (+ 1/4 (* 1/8 (/ eps x)))))>
#<alt (+ (* 1/2 x) (* eps (+ 1/4 (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))))))>
#<alt (* -1 (/ (pow x 2) eps))>
#<alt (/ (+ (* -2 (/ (pow x 3) eps)) (* -1 (pow x 2))) eps)>
#<alt (/ (- (+ (* -4 (/ (pow x 4) (pow eps 2))) (* -1 (pow x 2))) (* 2 (/ (pow x 3) eps))) eps)>
#<alt (/ (- (+ (* -8 (/ (pow x 5) (pow eps 3))) (* -1 (pow x 2))) (+ (* 2 (/ (pow x 3) eps)) (* 4 (/ (pow x 4) (pow eps 2))))) eps)>
#<alt (* -1 (/ (pow x 2) eps))>
#<alt (* -1 (/ (+ (* 2 (/ (pow x 3) eps)) (pow x 2)) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 5) eps)) (* -4 (pow x 4))) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))>
#<alt (* -1 eps)>
#<alt (- (* 2 x) eps)>
#<alt (- (* 2 x) eps)>
#<alt (- (* 2 x) eps)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1 (/ eps x))))>
#<alt (* x (+ 2 (* -1 (/ eps x))))>
#<alt (* x (+ 2 (* -1 (/ eps x))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (/ eps x) 2)))>
#<alt (* -1 (* x (- (/ eps x) 2)))>
#<alt (* -1 (* x (- (/ eps x) 2)))>
#<alt (* 2 x)>
#<alt (+ (* -1 eps) (* 2 x))>
#<alt (+ (* -1 eps) (* 2 x))>
#<alt (+ (* -1 eps) (* 2 x))>
#<alt (* -1 eps)>
#<alt (* eps (- (* 2 (/ x eps)) 1))>
#<alt (* eps (- (* 2 (/ x eps)) 1))>
#<alt (* eps (- (* 2 (/ x eps)) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1 (* -2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1 (* -2 (/ x eps)))))>

Calls

132 calls:

Time	Variable		Point	Expression
27.0ms	x	@	0	(cos x)
4.0ms	x	@	0	(- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x))))
3.0ms	eps	@	0	(- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x))))
3.0ms	x	@	-inf	(* (* (sin (* (- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x)))) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
2.0ms	x	@	inf	(* (* (sin (* (- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x)))) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

simplify493.0ms (3.4%)

Memory

-12.8MiB live, 385.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 782×	`lower-fma.f64`
10 782×	`lower-fma.f32`
6 862×	`lower-*.f64`
6 862×	`lower-*.f32`
4 164×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	870	8378
1	2613	7659
2	7926	7650
0	8192	7135

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 504

Calls

Call 1

Inputs
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(+ (sin x) (sin (neg x)))
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin 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)))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(sin eps)
(sin eps)
(sin eps)
(sin eps)
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1
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(cos x)
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
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(* 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 (+ eps x)) (sin x))
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(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
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eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(sin eps)
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eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* -1/6 (pow eps 3))
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(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
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(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* eps (cos x))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
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(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
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(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
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(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
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(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
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(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(/ 1 (sin eps))
(+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
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(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (- (sin (- eps (* -1 x))) (sin x)))
(/ 1 (* eps (cos x)))
(/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (+ eps x)) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(/ 1 (- (sin (- x (* -1 eps))) (sin x)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
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)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
eps
eps
eps
eps
eps
(- (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) x)) (+ (* -1 eps) (+ (* -1/8 (/ (pow eps 2) x)) (* 1/2 (/ (pow eps 2) x)))))
(- (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) x)) (* -1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 2)))) (+ (* -1 eps) (+ (* -1/8 (/ (pow eps 2) x)) (+ (* -1/16 (/ (pow eps 3) (pow x 2))) (* 1/2 (/ (pow eps 2) x))))))
(- (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) x)) (+ (* -1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 2))) (* -1/4 (/ (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 3))))) (+ (* -1 eps) (+ (* -1/8 (/ (pow eps 2) x)) (+ (* -1/16 (/ (pow eps 3) (pow x 2))) (+ (* -1/32 (/ (pow eps 4) (pow x 3))) (* 1/2 (/ (pow eps 2) x)))))))
(- (* 1/4 eps) (* -1 (- eps (* 1/4 eps))))
(- (+ (* -1 (/ (- (* -1/8 (pow eps 2)) (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) x)) (* 1/4 eps)) (* -1 (- eps (* 1/4 eps))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (pow eps 3)) (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))))) x)) (* -1/8 (pow eps 2))) (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) x)) (* 1/4 eps)) (* -1 (- eps (* 1/4 eps))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (pow eps 4)) (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))))) x)) (* 1/16 (pow eps 3))) (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))))) x)) (* -1/8 (pow eps 2))) (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) x)) (* 1/4 eps)) (* -1 (- eps (* 1/4 eps))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(+ (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x))
(+ (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (+ (* 2 (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2))) (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)))
(+ (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (+ (* 2 (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/4 (* (sin (* 1/2 eps)) (* (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3)))))) (* (cos (* 1/2 eps)) (+ (* -1/48 (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 3)) (* 1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/32 (pow eps 4)))))))) (pow x 3))) (+ (* 2 (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2))) (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))
(+ (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))) (/ (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))) x))
(+ (* -1 (/ (+ (* -2 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2))))) x)) (* -1 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))))) x)) (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))))
(+ (* -1 (/ (+ (* -1 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2)))))) (* -1 (/ (+ (* -2 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/4 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3)))))) (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (+ (* -1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* -1/32 (pow eps 4)))) (* 1/48 (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 3)))))) x)) (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2))))))) x))) x)) (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps)))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps)))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps)))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps)))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x))))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x))))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x))))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x))))))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (+ (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2))))
(+ (* 1/2 (/ (* (cos (* 1/2 eps)) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))))) x)) (+ (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) (+ (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/4 (* (sin (* 1/2 eps)) (* (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3)))))) (* (cos (* 1/2 eps)) (+ (* -1/48 (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 3)) (* 1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/32 (pow eps 4)))))))) (pow x 3)) (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/2 eps)) (pow (- (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))) (+ (* -1/8 (pow eps 2)) (* 1/2 (pow eps 2)))) 2))) (* 1/2 (* (cos (* 1/2 eps)) (- (* -1/2 (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps))))))) (* -1/16 (pow eps 3))))))) (pow x 2)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))
(+ (* 1/2 (/ (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))
(+ (* -1 (/ (+ (* -1 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2))))) x)) (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/4 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3)))))) (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (+ (* -1/2 (- (* -1/4 (* (pow eps 2) (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* -1/32 (pow eps 4)))) (* 1/48 (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 3)))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (- (* 1/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps))))))) (* 1/16 (pow eps 3))))) (* -1/8 (* (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (pow (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))) 2)))))) x)) (* -1/2 (* (cos (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))) (* (cos (* 1/2 (- eps (* -2 x)))) (- (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/8 (pow eps 2))))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow x 2) (- (* 2 x) eps)) (/ (pow (- eps x) 2) (- (* 2 x) eps))))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow x 2) (+ (* -1 eps) (* 2 x))) (/ (pow (+ x (* -1 eps)) 2) (+ (* -1 eps) (* 2 x)))))))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 3))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(* 1/2 x)
(+ (* -3/4 eps) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* 1/8 (/ eps x)) 3/4)))
(+ (* 1/2 x) (* eps (- (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))) 3/4)))
(* -1 eps)
(* eps (- (* -1 (/ (pow x 2) (pow eps 2))) 1))
(* eps (- (+ (* -2 (/ (pow x 3) (pow eps 3))) (* -1 (/ (pow x 2) (pow eps 2)))) 1))
(* eps (- (+ (* -4 (/ (pow x 4) (pow eps 4))) (* -1 (/ (pow x 2) (pow eps 2)))) (+ 1 (* 2 (/ (pow x 3) (pow eps 3))))))
(* -1 eps)
(* -1 (* eps (+ 1 (/ (pow x 2) (pow eps 2)))))
(* -1 (* eps (+ 1 (+ (* 2 (/ (pow x 3) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))
(* -1 (* eps (+ 1 (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))
(* -1 eps)
(+ (* -1 eps) (* -1 (/ (pow x 2) eps)))
(+ (* -1 eps) (* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps))))
(+ (* -1 eps) (* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))))
(* 1/2 x)
(* x (- (+ 1/2 (* -1 (/ eps x))) (* -1/4 (/ eps x))))
(* x (- (+ 1/2 (+ (* -1 (/ eps x)) (* 1/2 (/ (pow eps 2) (pow x 2))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))
(* x (- (+ 1/2 (+ (* -1 (/ eps x)) (+ (* 1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 3))) (* 1/2 (/ (pow eps 2) (pow x 2)))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))
(* 1/2 x)
(* -1 (* x (- (/ eps x) (+ 1/2 (* 1/4 (/ eps x))))))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (- eps (* 1/4 eps))) (* 1/2 (/ (pow eps 2) x))) (* 1/2 (/ (* eps (- eps (* 1/4 eps))) x))) x)) 1/2)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (- eps (* 1/4 eps))) (* -1 (/ (+ (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) x))) x))) x)) 1/2)))
(* -1 (/ (pow x 2) eps))
(* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps)))
(* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))
(* (pow x 2) (- (* x (- (* x (- (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))
(* 1/2 x)
(* x (+ 1/2 (* 1/4 (/ eps x))))
(* x (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* -1/4 (/ eps x))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/4 (/ eps x)) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(* 1/2 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/2)))
(* -1 (* x (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* -1/4 eps)) x)) 1/2)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* -1/4 eps)) x)) 1/2)))
(* 1/2 x)
(+ (* 1/4 eps) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ 1/4 (* 1/8 (/ eps x)))))
(+ (* 1/2 x) (* eps (+ 1/4 (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))))))
(* -1 (/ (pow x 2) eps))
(/ (+ (* -2 (/ (pow x 3) eps)) (* -1 (pow x 2))) eps)
(/ (- (+ (* -4 (/ (pow x 4) (pow eps 2))) (* -1 (pow x 2))) (* 2 (/ (pow x 3) eps))) eps)
(/ (- (+ (* -8 (/ (pow x 5) (pow eps 3))) (* -1 (pow x 2))) (+ (* 2 (/ (pow x 3) eps)) (* 4 (/ (pow x 4) (pow eps 2))))) eps)
(* -1 (/ (pow x 2) eps))
(* -1 (/ (+ (* 2 (/ (pow x 3) eps)) (pow x 2)) eps))
(* -1 (/ (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 5) eps)) (* -4 (pow x 4))) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))
(* -1 eps)
(- (* 2 x) eps)
(- (* 2 x) eps)
(- (* 2 x) eps)
(* 2 x)
(* x (+ 2 (* -1 (/ eps x))))
(* x (+ 2 (* -1 (/ eps x))))
(* x (+ 2 (* -1 (/ eps x))))
(* 2 x)
(* -1 (* x (- (/ eps x) 2)))
(* -1 (* x (- (/ eps x) 2)))
(* -1 (* x (- (/ eps x) 2)))
(* 2 x)
(+ (* -1 eps) (* 2 x))
(+ (* -1 eps) (* 2 x))
(+ (* -1 eps) (* 2 x))
(* -1 eps)
(* eps (- (* 2 (/ x eps)) 1))
(* eps (- (* 2 (/ x eps)) 1))
(* eps (- (* 2 (/ x eps)) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))

Outputs
(* x (- (cos eps) 1))
(fma.f64 x (cos.f64 eps) (neg.f64 x))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(fma.f64 x (fma.f64 x (*.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64))) (cos.f64 eps)) (neg.f64 x))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) (fma.f64 (.f64 x x) (fma.f64 (cos.f64 eps) #s(literal 1/120 binary64) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (cos.f64 eps)) (neg.f64 x))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/5040 binary64) #s(literal 1/5040 binary64))) (fma.f64 (cos.f64 eps) #s(literal 1/120 binary64) #s(literal -1/120 binary64))) #s(literal 1/6 binary64))) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin x) (sin (neg x)))
(-.f64 (sin.f64 x) (sin.f64 x))
(+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))
(fma.f64 eps (.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(+ (sin x) (sin (neg x)))
(-.f64 (sin.f64 x) (sin.f64 x))
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(fma.f64 eps (cos.f64 x) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x)) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) (-.f64 (sin.f64 x) (sin.f64 x)))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (cos.f64 eps))) (sin.f64 eps))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 (neg.f64 x))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 eps (.f64 eps (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (cos.f64 eps))) (sin.f64 eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (cos.f64 x)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 eps (.f64 eps (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* -1/6 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))
(* -1/6 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
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(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* -1/2 (- (* -1 (- eps (* 1/4 eps))) (* 1/4 eps)))))
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(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
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1
#s(literal 1 binary64)
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(cos eps)
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(* eps (- (* 1/3840 (pow eps 2)) 1/48))
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(* eps (- (* 1/3840 (pow eps 2)) 1/48))
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(* 1/3840 (pow eps 3))
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(* 1/3840 (pow eps 3))
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(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 eps))
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(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
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(fma.f64 x #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/4 binary64)))
(+ (* 1/2 x) (* eps (- (* 1/8 (/ eps x)) 3/4)))
(fma.f64 eps (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) #s(literal -3/4 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (* eps (- (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))) 3/4)))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1/8 binary64) x)) #s(literal -3/4 binary64)) (.f64 x #s(literal 1/2 binary64)))
(* -1 eps)
(neg.f64 eps)
(* eps (- (* -1 (/ (pow x 2) (pow eps 2))) 1))
(neg.f64 (fma.f64 eps (.f64 x (/.f64 x (.f64 eps eps))) eps))
(* eps (- (+ (* -2 (/ (pow x 3) (pow eps 3))) (* -1 (/ (pow x 2) (pow eps 2)))) 1))
(fma.f64 eps (-.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))) (.f64 x (/.f64 x (*.f64 eps eps)))) (neg.f64 eps))
(* eps (- (+ (* -4 (/ (pow x 4) (pow eps 4))) (* -1 (/ (pow x 2) (pow eps 2)))) (+ 1 (* 2 (/ (pow x 3) (pow eps 3))))))
(.f64 eps (-.f64 (-.f64 (/.f64 (.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 eps (.f64 eps eps)) eps)) (.f64 x (/.f64 x (.f64 eps eps)))) (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 2 binary64) (.f64 eps (*.f64 eps eps))) #s(literal 1 binary64))))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (/ (pow x 2) (pow eps 2)))))
(neg.f64 (fma.f64 eps (.f64 x (/.f64 x (.f64 eps eps))) eps))
(* -1 (* eps (+ 1 (+ (* 2 (/ (pow x 3) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))
(.f64 (neg.f64 eps) (fma.f64 x (/.f64 x (.f64 eps eps)) (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 2 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64))))
(* -1 (* eps (+ 1 (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) (pow eps 3))) (/ (pow x 2) (pow eps 2))))))
(neg.f64 (fma.f64 eps (-.f64 (.f64 x (/.f64 x (.f64 eps eps))) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x (.f64 x x)) (/.f64 (.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64))) eps)) (.f64 eps (*.f64 eps eps)))) eps))
(* -1 eps)
(neg.f64 eps)
(+ (* -1 eps) (* -1 (/ (pow x 2) eps)))
(neg.f64 (fma.f64 x (/.f64 x eps) eps))
(+ (* -1 eps) (* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps))))
(fma.f64 (.f64 x x) (fma.f64 x (/.f64 #s(literal -2 binary64) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps))
(+ (* -1 eps) (* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))))
(fma.f64 (.f64 x x) (fma.f64 x (fma.f64 #s(literal -4 binary64) (/.f64 x (.f64 eps (.f64 eps eps))) (/.f64 #s(literal -2 binary64) (.f64 eps eps))) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (- (+ 1/2 (* -1 (/ eps x))) (* -1/4 (/ eps x))))
(*.f64 x (fma.f64 (/.f64 eps x) #s(literal -3/4 binary64) #s(literal 1/2 binary64)))
(* x (- (+ 1/2 (+ (* -1 (/ eps x)) (* 1/2 (/ (pow eps 2) (pow x 2))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))
(.f64 x (+.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 eps x)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (-.f64 eps (.f64 #s(literal 3/4 binary64) eps)))) (.f64 x x))) (/.f64 (.f64 eps #s(literal 1/4 binary64)) x)))
(* x (- (+ 1/2 (+ (* -1 (/ eps x)) (+ (* 1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* -1/2 (* eps (- (* -1 eps) (* -1/4 eps)))))) (pow x 3))) (* 1/2 (/ (pow eps 2) (pow x 2)))))) (+ (* -1/2 (/ (* eps (- (* -1 eps) (* -1/4 eps))) (pow x 2))) (* -1/4 (/ eps x)))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 eps (/.f64 eps (.f64 x x)) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal 3/4 binary64) eps)))) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (fma.f64 (.f64 eps (.f64 eps #s(literal -3/4 binary64))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 eps #s(literal -1/4 binary64)) x))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (/ eps x) (+ 1/2 (* 1/4 (/ eps x))))))
(.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 3/4 binary64) eps) x) #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (- eps (* 1/4 eps))) (* 1/2 (/ (pow eps 2) x))) (* 1/2 (/ (* eps (- eps (* 1/4 eps))) x))) x)) 1/2)))
(.f64 (neg.f64 x) (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 3/4 binary64) eps (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (-.f64 eps (.f64 #s(literal 3/4 binary64) eps)))) x)) x)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (- eps (* 1/4 eps))) (* -1 (/ (+ (* -1 (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) (* -1/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* 1/2 (* eps (- eps (* 1/4 eps)))))) x))) x))) x)) 1/2)))
(neg.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (.f64 eps #s(literal -3/4 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal 3/4 binary64) eps)))) x) (.f64 #s(literal -1/2 binary64) (.f64 eps (-.f64 eps (*.f64 #s(literal 3/4 binary64) eps))))) x)) (neg.f64 x)))))
(* -1 (/ (pow x 2) eps))
(neg.f64 (/.f64 (*.f64 x x) eps))
(* (pow x 2) (- (* -2 (/ x (pow eps 2))) (/ 1 eps)))
(.f64 (.f64 x x) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(* (pow x 2) (- (* x (- (* -4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 #s(literal -4 binary64) (/.f64 x (.f64 eps (.f64 eps eps))) (/.f64 #s(literal -2 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1 binary64) eps)))
(* (pow x 2) (- (* x (- (* x (- (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps)))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -8 binary64) (/.f64 x (.f64 (.f64 eps (.f64 eps eps)) eps)) (/.f64 #s(literal -4 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal -2 binary64) (.f64 eps eps))) (/.f64 #s(literal -1 binary64) eps)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 eps x) #s(literal 1/2 binary64)))
(* x (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* -1/4 (/ eps x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64))) x)))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/4 (/ eps x)) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(.f64 x (-.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 eps #s(literal -1/4 binary64)) x))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/2)))
(neg.f64 (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/4 binary64) x) #s(literal -1/2 binary64))))
(* -1 (* x (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* -1/4 eps)) x)) 1/2)))
(.f64 (neg.f64 x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64))) (neg.f64 x))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* -1/4 eps)) x)) 1/2)))
(.f64 (neg.f64 x) (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 eps #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) x) (.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (neg.f64 x))) (neg.f64 x))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/4 eps) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/4 binary64)))
(+ (* 1/2 x) (* eps (+ 1/4 (* 1/8 (/ eps x)))))
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (* eps (+ 1/4 (* eps (+ (* 1/16 (/ eps (pow x 2))) (* 1/8 (/ 1 x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/2 binary64)))
(* -1 (/ (pow x 2) eps))
(neg.f64 (/.f64 (*.f64 x x) eps))
(/ (+ (* -2 (/ (pow x 3) eps)) (* -1 (pow x 2))) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x x)) eps) (*.f64 x x)) (neg.f64 eps))
(/ (- (+ (* -4 (/ (pow x 4) (pow eps 2))) (* -1 (pow x 2))) (* 2 (/ (pow x 3) eps))) eps)
(/.f64 (fma.f64 x (neg.f64 x) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x (.f64 x x)) (/.f64 (*.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64))) eps)) eps)) eps)
(/ (- (+ (* -8 (/ (pow x 5) (pow eps 3))) (* -1 (pow x 2))) (+ (* 2 (/ (pow x 3) eps)) (* 4 (/ (pow x 4) (pow eps 2))))) eps)
(/.f64 (+.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 x (.f64 x x)) eps)) (.f64 x x))) (/.f64 (.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 eps eps))) eps)
(* -1 (/ (pow x 2) eps))
(neg.f64 (/.f64 (*.f64 x x) eps))
(* -1 (/ (+ (* 2 (/ (pow x 3) eps)) (pow x 2)) eps))
(/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x x)) eps) (*.f64 x x)) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (* -4 (/ (pow x 4) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))
(/.f64 (-.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x (.f64 x x)) (/.f64 (.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64))) eps)) eps)) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 5) eps)) (* -4 (pow x 4))) eps)) (* 2 (pow x 3))) eps)) (pow x 2)) eps))
(/.f64 (-.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal -2 binary64) (.f64 x (.f64 x x)) (/.f64 (fma.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 8 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) eps))) (neg.f64 eps))) eps)) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (* 2 x) eps)
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(- (* 2 x) eps)
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(- (* 2 x) eps)
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1 (/ eps x))))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (* -1 (/ eps x))))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (* -1 (/ eps x))))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (/ eps x) 2)))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (/ eps x) 2)))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (/ eps x) 2)))
(*.f64 x (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1 eps) (* 2 x))
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(+ (* -1 eps) (* 2 x))
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(+ (* -1 eps) (* 2 x))
(-.f64 (*.f64 x #s(literal 2 binary64)) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (* 2 (/ x eps)) 1))
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (* 2 (/ x eps)) 1))
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (* 2 (/ x eps)) 1))
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))
(*.f64 (neg.f64 eps) (fma.f64 x (/.f64 #s(literal -2 binary64) eps) #s(literal 1 binary64)))
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))
(*.f64 (neg.f64 eps) (fma.f64 x (/.f64 #s(literal -2 binary64) eps) #s(literal 1 binary64)))
(* -1 (* eps (+ 1 (* -2 (/ x eps)))))
(*.f64 (neg.f64 eps) (fma.f64 x (/.f64 #s(literal -2 binary64) eps) #s(literal 1 binary64)))

rewrite413.0ms (2.9%)

Memory

11.0MiB live, 436.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 056×	`lower-*.f32`
4 044×	`lower-/.f32`
4 036×	`lower-/.f64`
4 028×	`lower-*.f64`
3 790×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	401
0	112	367
1	418	328
2	3702	328
0	9109	325

Stop Event

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

Counts

26 → 610

Calls

Call 1

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

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

eval181.0ms (1.3%)

Memory: 2.4MiB live, 399.3MiB allocated
Compiler: Compiled 36 519 to 3 979 computations (89.1% saved)

prune175.0ms (1.2%)

Memory

-7.2MiB live, 312.7MiB allocated

Pruning

29 alts after pruning (21 fresh and 8 done)

	Pruned	Kept	Total
New	1 174	12	1 186
Fresh	3	9	12
Picked	1	4	5
Done	0	4	4
Total	1 178	29	1 207

Accuracy

100.0%

Counts

1 207 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (*.f64 eps (cos.f64 x))))))
✓	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
	96.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) x) eps)))))
	97.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 x (.f64 (.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64)))) eps)))))
	97.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))))
✓	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	36.4%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (-.f64 eps x) (neg.f64 (/.f64 (-.f64 eps x) (+.f64 x (-.f64 x eps)))) (/.f64 (.f64 x x) (+.f64 x (-.f64 x eps)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	21.1%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (+.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (+.f64 eps x))) (.f64 x x))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	35.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (.f64 x x)) (-.f64 (-.f64 eps x) x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	18.3%	(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (/.f64 (-.f64 (.f64 (-.f64 x eps) (-.f64 x eps)) (.f64 x x)) (-.f64 (-.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	35.5%	(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	63.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	73.6%	(.f64 (.f64 (sin.f64 (.f64 #s(approx (/ (- (pow (+ x eps) 3) ( x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x)))) (fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64))) eps) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
✓	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.1%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	98.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	98.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	5.5%	#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
	98.7%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)))))
	98.2%	#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	50.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
	28.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))))))
	44.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))))
	5.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
	99.7%	#s(approx (* (* (sin (* (- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x)))) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (fma.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (/.f64 (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps #s(literal -3/4 binary64))) (.f64 (*.f64 eps eps) #s(literal -3/8 binary64)))) x)))

Compiler

Compiled 1 567 to 620 computations (60.4% saved)

regimes44.0ms (0.3%)

Memory

-16.1MiB live, 79.0MiB allocated

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 x (.f64 (.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64)))) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))
#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (*.f64 eps (cos.f64 x))))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(approx (/ (- (pow (+ x eps) 3) ( x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x)))) (fma.f64 (neg.f64 eps) (/.f64 (fma.f64 x #s(literal 3 binary64) (.f64 x #s(literal -3 binary64))) eps) eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (.f64 x x)) (-.f64 (-.f64 eps x) x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 x (-.f64 eps x)))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (-.f64 eps x) (neg.f64 (/.f64 (-.f64 eps x) (+.f64 x (-.f64 x eps)))) (/.f64 (.f64 x x) (+.f64 x (-.f64 x eps)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (-.f64 (/.f64 (.f64 x x) (-.f64 x (-.f64 eps x))) (/.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (/.f64 (-.f64 (.f64 (-.f64 x eps) (-.f64 x eps)) (.f64 x x)) (-.f64 (-.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (-.f64 x (+.f64 eps x)))) eps) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 eps x)) eps)) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 eps x)) (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (-.f64 x (+.f64 eps x)))) eps))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (+.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x (+.f64 eps x))) (.f64 x x))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 #s(approx (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
#s(approx (* (* (sin (* (- (/ (* x x) (- x (- eps x))) (/ (* (- eps x) (- eps x)) (- x (- eps x)))) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (fma.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (/.f64 (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps #s(literal -3/4 binary64))) (.f64 (*.f64 eps eps) #s(literal -3/8 binary64)))) x)))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))

Outputs

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

Calls

3 calls:

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

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 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

5.8MiB live, 41.9MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 x (.f64 (.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64)))) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

7.7MiB live, 46.9MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 x (.f64 (.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64)))) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (/ 1 (/ 1 (- (sin (+ x eps)) (sin x)))) (*.f64 eps (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

6.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	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 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-6.4MiB live, 38.0MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	eps
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	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 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-4.4MiB live, 35.3MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-9.8MiB live, 28.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

25.1MiB live, 25.1MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`x`
97.3%	1	`eps`
97.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

-16.2MiB live, 23.3MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`eps`
96.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

13.2MiB live, 13.2MiB allocated

Accuracy

Total -0.2b remaining (-0.3%)

Threshold costs -0.2b (-0.3%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.5%	1	`x`
5.5%	1	`eps`
5.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-20.9MiB live, 20.0MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	274
1	119	274

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (7.8%)

Memory

28.7MiB live, 936.2MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
11 388×	`lower-fma.f64`
11 388×	`lower-fma.f32`
10 782×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	870	8378
1	2613	7659
2	7926	7650
0	8192	7135
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	630	6892
1	2048	6206
2	7282	6173
0	8166	5757
0	590	5491
1	1815	5145
2	5276	4941
0	8688	4623

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

Compiler

Compiled 322 to 190 computations (41% saved)

preprocess155.0ms (1.1%)

Memory: -8.2MiB live, 193.9MiB allocated
Compiler: Compiled 342 to 176 computations (48.5% 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

analyze39.0ms (0.3%)

sample6.4s (44.2%)

preprocess28.0ms (0.2%)

explain93.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize23.0ms (0.2%)

series3.0ms (0%)

simplify508.0ms (3.5%)

rewrite454.0ms (3.1%)

eval201.0ms (1.4%)

prune39.0ms (0.3%)

simplify353.0ms (2.4%)

localize393.0ms (2.7%)

series37.0ms (0.3%)

simplify374.0ms (2.6%)

rewrite141.0ms (1%)

eval139.0ms (1%)

prune109.0ms (0.8%)

simplify284.0ms (2%)

localize429.0ms (3%)

series38.0ms (0.3%)

simplify397.0ms (2.8%)

rewrite184.0ms (1.3%)

eval136.0ms (0.9%)

prune124.0ms (0.9%)

simplify317.0ms (2.2%)

localize426.0ms (3%)

series71.0ms (0.5%)

simplify493.0ms (3.4%)

rewrite413.0ms (2.9%)

eval181.0ms (1.3%)

prune175.0ms (1.2%)

regimes44.0ms (0.3%)

regimes24.0ms (0.2%)

regimes18.0ms (0.1%)

regimes18.0ms (0.1%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0%)

simplify10.0ms (0.1%)

soundness1.1s (7.8%)

preprocess155.0ms (1.1%)

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