Metrics for 2sin (example 3.3)

analyze60.0ms (0.4%)

Memory

1.8MiB live, 39.9MiB 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)

sample6.2s (41.4%)

Memory

-244.9MiB live, 6 987.0MiB allocated

Samples

3.4s	26 402×	0	invalid
638.0ms	5 491×	0	valid
485.0ms	2 765×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

const: 944.0ms (29% of total)

ival-sin: 556.0ms (17.1% of total)

ival-add: 374.0ms (11.5% of total)

ival-fabs: 287.0ms (8.8% of total)

ival-mult: 280.0ms (8.6% of total)

ival-<=: 216.0ms (6.6% of total)

ival-sub: 209.0ms (6.4% of total)

ival-<: 152.0ms (4.7% of total)

ival-and: 101.0ms (3.1% of total)

adjust: 78.0ms (2.4% of total)

exact: 46.0ms (1.4% of total)

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

Bogosity

preprocess28.0ms (0.2%)

Memory

-5.3MiB live, 33.5MiB 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))

explain86.0ms (0.6%)

Memory

4.0MiB live, 81.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
226	1	(7.958824461753575e-106 4.375907447766258e-108)	2	(-1.232819322890588e-264 1.8430614345278302e-266)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	225	4
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	224	2
-	1	29

Precision

0.9955555555555555

Recall

0.9911504424778761

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	224	2	0
-	1	2	27

Precision?

0.9868995633187773

Recall?

1.0

Freqs

test

number	freq
0	31
1	224
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	362×	0	valid
15.0ms	150×	1	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sin: 9.0ms (50.3% of total)

adjust: 3.0ms (16.8% of total)

ival-sub: 3.0ms (16.8% of total)

ival-add: 3.0ms (16.8% of total)

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

ival-assert: 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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB 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

21.4MiB live, 21.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	64.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

8.0ms	181×	0	valid
7.0ms	75×	1	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 (46.1% of total)

ival-add: 2.0ms (23.1% of total)

adjust: 1.0ms (11.5% of total)

ival-sub: 1.0ms (11.5% of total)

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

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

series42.0ms (0.3%)

Memory

-37.0MiB live, 4.4MiB 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
38.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
1.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))
1.0ms	eps	@	inf	(- (sin (+ x eps)) (sin x))
0.0ms	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(sin x)

simplify457.0ms (3.1%)

Memory

32.6MiB live, 303.5MiB 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)

rewrite590.0ms (4%)

Memory

-39.6MiB live, 337.6MiB 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))

eval36.0ms (0.2%)

Memory: 2.8MiB live, 77.3MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune31.0ms (0.2%)

Memory

37.8MiB live, 76.9MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	286	6	292

Accuracy

100.0%

Counts

292 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	64.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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))
▶	99.9%	#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)))))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 135 to 88 computations (34.8% saved)

simplify450.0ms (3%)

Memory

-0.7MiB live, 440.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

7 672×	`lower-fma.f32`
7 664×	`lower-fma.f64`
6 264×	`lower-*.f32`
6 244×	`lower-*.f64`
2 444×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	234
0	59	224
1	98	224
2	221	224
3	443	220
4	714	220
5	875	220
6	1024	220
7	1249	220
8	1341	220
9	1361	220
10	1527	220
11	1863	220
12	2174	220
13	2961	220
14	3798	220
15	4039	220
16	4147	220
17	4393	220
18	4606	220
19	4610	220
20	4692	220
21	4762	220
22	4762	220
23	4762	220
24	4940	220
25	5008	220
26	5008	220
27	5008	220
28	5008	220
29	7172	220
0	8088	213

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

localize128.0ms (0.9%)

Memory

-11.6MiB live, 220.7MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.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))))
✓	accuracy	99.9%	#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)))))
✓	accuracy	99.5%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.7%	#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%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	97.8%	#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%	(.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	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #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

44.0ms	182×	0	valid
32.0ms	74×	1	valid

Compiler

Compiled 212 to 36 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 23.0ms (41.9% of total)

ival-add: 8.0ms (14.6% of total)

ival-sin: 7.0ms (12.8% of total)

adjust: 6.0ms (10.9% of total)

ival-cos: 4.0ms (7.3% of total)

const: 4.0ms (7.3% of total)

ival-sub: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series32.0ms (0.2%)

Memory

17.6MiB live, 53.0MiB allocated

Counts

20 → 396

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

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))))))))))>
#<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 (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 (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 (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<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 (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin 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 (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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<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 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)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>

Calls

99 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))))
1.0ms	x	@	-inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))

simplify411.0ms (2.8%)

Memory

-30.3MiB live, 570.1MiB allocated

Algorithm

1×	egg-herbie

Rules

17 506×	`lower-fma.f64`
17 506×	`lower-fma.f32`
6 192×	`lower-*.f64`
6 192×	`lower-*.f32`
4 722×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	3903
1	1243	3731
2	3512	3683
0	8152	3378

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 377

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

rewrite348.0ms (2.3%)

Memory

36.3MiB live, 395.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 260×	`lower-fma.f32`
6 252×	`lower-fma.f64`
4 170×	`lower-*.f32`
4 150×	`lower-*.f64`
3 838×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	184
0	59	176
1	194	176
2	1639	176
0	8082	176

Stop Event

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

Counts

20 → 590

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

Outputs
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 eps eps) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
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eps
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#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
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(sin.f64 eps)
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#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
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(fma.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps) (.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps) (.f64 #s(literal 0 binary64) (cos.f64 x)))
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(/.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (cos.f64 x) (.f64 eps eps)) eps)
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eval125.0ms (0.8%)

Memory: -2.6MiB live, 182.6MiB allocated
Compiler: Compiled 25 897 to 2 278 computations (91.2% saved)

prune137.0ms (0.9%)

Memory

1.3MiB live, 163.5MiB allocated

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	1 003	16	1 019
Fresh	0	0	0
Picked	2	3	5
Done	1	0	1
Total	1 006	19	1 025

Accuracy

100.0%

Counts

1 025 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.1%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps eps)) (/.f64 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))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.8%	(.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))
▶	99.7%	(.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%	#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)))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 550 to 319 computations (42% saved)

simplify666.0ms (4.5%)

Memory

-20.5MiB live, 538.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

24 504×	`lower-fma.f32`
24 494×	`lower-fma.f64`
3 916×	`lower-*.f32`
3 888×	`lower-*.f64`
2 680×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	462
0	81	450
1	150	450
2	403	450
3	1064	442
4	1543	442
5	1952	442
6	2230	442
7	2277	442
8	2371	442
9	2563	442
10	2950	442
11	3588	442
12	4008	442
13	5162	442
14	5813	442
15	6190	442
16	6438	442
17	6522	442
18	6531	442
19	7263	442
20	7440	442
21	7453	442
22	7457	442
23	7463	442
24	7467	442
25	7467	442
0	8387	418

Stop Event

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

Calls

Call 1

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

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

localize182.0ms (1.2%)

Memory

32.8MiB live, 277.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.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))))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) eps)
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))
✓	accuracy	97.8%	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))
✓	accuracy	100.0%	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))
✓	accuracy	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
✓	accuracy	99.5%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	97.8%	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
✓	accuracy	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
✓	accuracy	97.8%	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	#s(approx (sin (* (+ eps 0) 1/2)) (.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	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))

Samples

58.0ms	179×	0	valid
49.0ms	74×	1	valid
3.0ms	2×	5	exit
1.0ms	1×	3	valid

Compiler

Compiled 330 to 48 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-mult: 33.0ms (39.4% of total)

ival-add: 20.0ms (23.9% of total)

const: 11.0ms (13.1% of total)

adjust: 7.0ms (8.4% of total)

ival-sin: 6.0ms (7.2% of total)

ival-cos: 4.0ms (4.8% of total)

ival-sub: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series16.0ms (0.1%)

Memory

-9.8MiB live, 26.8MiB allocated

Counts

23 → 468

Calls

Call 1

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

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 (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)>
#<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 (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 (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin 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 (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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))>
#<alt (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps)))))>
#<alt (+ eps (* -1/6 (pow eps 3)))>
#<alt (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))>
#<alt (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))>
#<alt (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))>
#<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 (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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))>
#<alt (* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))>
#<alt (* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (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)>
#<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 (* -1/48 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 (* 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 (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>

Calls

117 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2))))
0.0ms	x	@	inf	(+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2))))
0.0ms	eps	@	0	(* eps (+ (* (* eps eps) 1/3840) -1/48))
0.0ms	eps	@	inf	(* eps (+ (* (* eps eps) 1/3840) -1/48))
0.0ms	eps	@	inf	(+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2))))

simplify504.0ms (3.4%)

Memory

20.8MiB live, 653.1MiB allocated

Algorithm

1×	egg-herbie

Rules

18 726×	`lower-fma.f64`
18 726×	`lower-fma.f32`
6 502×	`lower-*.f64`
6 502×	`lower-*.f32`
4 350×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	5437
1	1220	5135
2	3564	5072
0	8239	4650

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 463

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 (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)))
(* 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))
(* 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)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* 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) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
eps
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))
(* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps)))))
(* -1 (* (pow eps 3) (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps)))))
(+ eps (* -1/6 (pow eps 3)))
(+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))
(+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))
(+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))
(* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))
(* x (+ (* -1/2 (pow eps 2)) (+ (* -1/6 (/ (pow eps 3) x)) (/ eps x))))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2)))))
(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) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))
(* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))
(* (pow eps 2) (+ (* -1/2 x) (* -1/6 eps)))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))
(* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))
(* (pow eps 3) (- (* -1/2 (/ x eps)) 1/6))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/6 (* 1/2 (/ x eps)))))
(* -1/6 (pow eps 3))
(+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))
(+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))
(+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))
(* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))
(* x (+ (* -1/2 (pow eps 2)) (* -1/6 (/ (pow eps 3) x))))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* 1/6 (/ (pow eps 3) x)) (* 1/2 (pow eps 2)))))
(* 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)))
(* 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))
(* -1/48 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 (* 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))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 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 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
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 (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 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 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(* 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 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) 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))))))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (neg.f64 x) #s(literal 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 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 1/2 (* eps (cos x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
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(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 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 (sin.f64 x) #s(literal -1/4 binary64) (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/12 binary64))) (.f64 #s(literal 1/2 binary64) (cos.f64 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))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (neg.f64 x) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.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 (+ 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 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(* 1/3840 (pow eps 3))
(.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* 1/3840 (pow eps 3))
(.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)

rewrite308.0ms (2.1%)

Memory

-30.4MiB live, 491.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 158×	`lower-*.f32`
4 136×	`lower-/.f64`
4 136×	`lower-/.f32`
4 130×	`lower-*.f64`
3 702×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	380
0	81	368
1	292	368
2	2580	368
0	8140	357

Stop Event

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

Counts

23 → 480

Calls

Call 1

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

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

eval231.0ms (1.5%)

Memory: 11.1MiB live, 197.0MiB allocated
Compiler: Compiled 28 381 to 2 303 computations (91.9% saved)

prune101.0ms (0.7%)

Memory

29.4MiB live, 227.2MiB allocated

Pruning

21 alts after pruning (16 fresh and 5 done)

	Pruned	Kept	Total
New	1 052	6	1 058
Fresh	1	10	11
Picked	3	2	5
Done	0	3	3
Total	1 056	21	1 077

Accuracy

100.0%

Counts

1 077 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.1%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps eps)) (/.f64 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))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.8%	(.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))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
✓	99.9%	#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)))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
▶	5.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
	31.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
▶	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 597 to 342 computations (42.7% saved)

simplify334.0ms (2.2%)

Memory

-28.8MiB live, 310.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
✓	cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
✓	cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
✓	cost-diff	832	(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
✓	cost-diff	0	(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))
✓	cost-diff	0	#s(approx (cos x) (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)))
✓	cost-diff	0	(.f64 eps #s(approx (cos x) (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))))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
✓	cost-diff	0	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
✓	cost-diff	0	#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
✓	cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
✓	cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
✓	cost-diff	0	(.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	#s(approx (sin (* (+ eps 0) 1/2)) (.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 ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Rules

6 424×	`lower-fma.f32`
6 410×	`lower-fma.f64`
4 840×	`lower-*.f32`
4 810×	`lower-*.f64`
3 298×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	600
0	103	585
1	206	585
2	592	585
3	1444	546
4	2155	546
5	2596	546
6	4367	546
7	5199	546
8	5773	546
9	5988	546
10	6228	546
11	6430	546
12	6677	546
0	8750	534

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (+ (* x 2) eps) 1/2) (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 (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
(.f64 eps #s(approx (cos x) (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))))
eps
#s(approx (cos x) (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)))
(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))
(*.f64 x 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))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)

Outputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (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)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #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(approx (sin (* (+ eps 0) 1/2)) (.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 (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 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 eps (.f64 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 eps (.f64 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 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (* (+ (* x 2) eps) 1/2) (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 (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))))
#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(*.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 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)))))
(.f64 eps #s(approx (cos x) (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))))
(.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 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))))
eps
#s(approx (cos x) (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)))
#s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 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)))
(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))
(fma.f64 x (.f64 x (fma.f64 x (.f64 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))
(*.f64 x 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))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #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)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (* (+ eps 0) 1/2)) (*.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 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 x eps)
x
#s(literal 2 binary64)

localize231.0ms (1.6%)

Memory

7.1MiB live, 317.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
✓	accuracy	99.9%	(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
✓	accuracy	99.7%	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	99.6%	(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
✓	accuracy	100.0%	(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))
✓	accuracy	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
✓	accuracy	98.6%	#s(approx (cos x) (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)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.8%	(*.f64 eps (+.f64 eps x))
✓	accuracy	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
✓	accuracy	98.2%	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))
✓	accuracy	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
✓	accuracy	97.8%	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
✓	accuracy	2.7%	#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
✓	accuracy	100.0%	#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	100.0%	#s(approx (sin (* (+ eps 0) 1/2)) (.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	99.9%	(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.5%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))

Samples

80.0ms	181×	0	valid
64.0ms	74×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 352 to 64 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-mult: 47.0ms (40.4% of total)

ival-add: 23.0ms (19.8% of total)

const: 19.0ms (16.3% of total)

adjust: 11.0ms (9.5% of total)

ival-cos: 6.0ms (5.2% of total)

ival-sin: 6.0ms (5.2% of total)

ival-div: 2.0ms (1.7% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series73.0ms (0.5%)

Memory

-10.9MiB live, 26.8MiB allocated

Counts

28 → 552

Calls

Call 1

Inputs
#<alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))>
#<alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (.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 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 #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))>
#<alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))>
#<alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))>
#<alt #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))>
#<alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))>
#<alt (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)>
#<alt (*.f64 x #s(literal -1/2 binary64))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))>
#<alt (.f64 eps #s(approx (cos x) (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))))>
#<alt #s(approx (cos x) (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)))>
#<alt (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))>
#<alt (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))>
#<alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))>
#<alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))>
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))>
#<alt (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))>
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (.f64 (.f64 eps eps) #s(literal -1/6 binary64))>
#<alt (*.f64 eps (+.f64 eps x))>
#<alt (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))>
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))>
#<alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))>

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)>
#<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 (* 1/2 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) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<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 (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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<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 (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 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 (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<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 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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<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 (* 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 (* 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)>
#<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 (* -1/48 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 (* 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 (+ 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 (* -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 x)>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (* eps x)>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* eps x)>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt 1/24>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<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>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (/ x eps)>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))>
#<alt (/ x eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt (/ (+ x (* 1/2 eps)) eps)>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt 1/2>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>
#<alt (+ 1/2 (/ x eps))>

Calls

138 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(+ (* (* x x) (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2)) 1)
1.0ms	eps	@	inf	(* eps (+ (* eps (* eps (+ (* (* eps eps) 1/3840) -1/48))) 1/2))
1.0ms	eps	@	-inf	(+ (* (* x -1/2) (* eps (+ eps x))) eps)
1.0ms	eps	@	inf	(+ (* (* x -1/2) (* eps (+ eps x))) eps)
1.0ms	eps	@	0	(+ (* (* x -1/2) (* eps (+ eps x))) eps)

simplify374.0ms (2.5%)

Memory

11.4MiB live, 605.2MiB allocated

Algorithm

1×	egg-herbie

Rules

15 400×	`lower-fma.f64`
15 400×	`lower-fma.f32`
6 996×	`lower-*.f64`
6 996×	`lower-*.f32`
4 098×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	425	5722
1	1335	5443
2	3800	5376
0	8393	4959

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 543

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))))
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
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(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))
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(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
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(- (sin (- eps (* -1 x))) (sin x))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(- (sin (+ eps x)) (sin x))
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1
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eps
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
eps
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(- (sin (- x (* -1 eps))) (sin x))
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
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(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
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(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
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x
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(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
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(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
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(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
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(* x (+ 1 (* 1/2 (/ eps x))))
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))))))))))
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(* (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)))
(* 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))
(* -1/48 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 (* 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)
(+ 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)))
(* -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))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(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
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))

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

rewrite399.0ms (2.7%)

Memory

21.3MiB live, 541.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 948×	`lower-*.f32`
5 918×	`lower-*.f64`
5 736×	`lower-fma.f32`
5 722×	`lower-fma.f64`
3 500×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	514
0	103	502
1	408	502
2	3733	502
0	9252	479

Stop Event

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

Counts

28 → 748

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (sin (* (+ eps 0) 1/2)) (.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)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(*.f64 x #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
(.f64 eps #s(approx (cos x) (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))))
#s(approx (cos x) (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)))
(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))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(*.f64 eps (+.f64 eps x))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))

Outputs
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (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)) (.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)))) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(approx (sin (* (+ eps 0) 1/2)) (.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 (.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* (+ eps 0) 1/2)) (.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)))))
#s(approx (sin (* (+ eps 0) 1/2)) (.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 (.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 (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)) #s(literal 0 binary64)))
(+.f64 (.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 #s(literal 0 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 (.f64 eps #s(literal 1/2 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (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)) #s(literal 0 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))))
(+.f64 (.f64 #s(literal 0 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) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))
(fma.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 (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)) #s(literal 0 binary64)))
(fma.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 #s(literal 0 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))))
(fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 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) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))
(fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 eps eps) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (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 (.f64 (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)) #s(literal 0 binary64)))
(fma.f64 (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 (.f64 #s(literal 0 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))))
(fma.f64 (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)) #s(literal 0 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))))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) eps (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) #s(literal 1/8 binary64))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 eps 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 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) #s(literal 1/8 binary64))) (.f64 eps (-.f64 (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal -1/4 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))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) #s(literal 1/8 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) #s(literal 1/8 binary64)) (.f64 eps eps)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) eps))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))) #s(literal -1/4 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (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 eps)))
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(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) x) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) x) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) x) (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal 0 binary64)))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) x) (.f64 eps eps) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 0 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) x) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) eps (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)))) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) eps)))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps eps) (.f64 eps (.f64 eps eps))))) (.f64 eps (.f64 eps (.f64 eps eps))))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) eps))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 eps (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (.f64 eps eps) (.f64 eps (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 0 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 x (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) eps (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)))) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps eps) (.f64 eps (.f64 eps eps))))) (.f64 eps (.f64 eps (.f64 eps eps))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) eps))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))) (.f64 eps (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal 0 binary64)))) (.f64 eps (fma.f64 (.f64 eps eps) (.f64 eps eps) (+.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (.f64 eps eps) (.f64 eps (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 0 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) x) (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 eps x) eps)
(+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x #s(literal -1/720 binary64)) x #s(literal 1/24 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (/.f64 (/.f64 (.f64 x x) (.f64 eps eps)) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(fma.f64 x (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 x eps) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (.f64 eps (.f64 eps eps))) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (*.f64 eps eps)) eps #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 eps eps)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (/.f64 (.f64 x x) (.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) eps))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 eps eps))) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))))) (neg.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 eps eps)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal 1/4 binary64)) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 eps eps)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))))

eval250.0ms (1.7%)

Memory: 24.2MiB live, 243.5MiB allocated
Compiler: Compiled 33 944 to 3 560 computations (89.5% saved)

prune277.0ms (1.9%)

Memory

-19.2MiB live, 275.9MiB allocated

Pruning

22 alts after pruning (14 fresh and 8 done)

	Pruned	Kept	Total
New	1 284	7	1 291
Fresh	4	7	11
Picked	2	3	5
Done	0	5	5
Total	1 290	22	1 312

Accuracy

100.0%

Counts

1 312 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.1%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps eps)) (/.f64 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))
✓	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.8%	(.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 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	99.9%	#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)))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
	31.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
✓	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
	51.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))))))
	5.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))

Compiler

Compiled 890 to 341 computations (61.7% saved)

regimes63.0ms (0.4%)

Memory

-31.6MiB live, 47.2MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 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 (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (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 #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 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #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 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (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 (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 (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 (.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)))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps eps)) (/.f64 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))

Outputs

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

Calls

3 calls:

30.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	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

37.8MiB live, 37.8MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 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 (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (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 #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 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #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 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

-21.1MiB live, 18.3MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 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 (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (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 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Calls

3 calls:

18.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 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 (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))

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

Calls

3 calls:

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

regimes26.0ms (0.2%)

Memory

-28.4MiB live, 12.2MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (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:

13.0ms	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

20.9MiB live, 20.9MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ eps (* (* eps eps) (+ (* eps -1/6) (* x -1/2)))) (.f64 (.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 (+.f64 eps x) (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (neg.f64 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

-18.9MiB live, 19.3MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* (* x -1/2) (* eps (+ eps x))) eps) (.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) (.f64 eps eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))

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

Calls

3 calls:

17.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

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)

regimes10.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.2%	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)

regimes24.0ms (0.2%)

Memory

-24.9MiB live, 13.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

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)

regimes7.0ms (0%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes6.0ms (0%)

Memory

11.0MiB live, 11.0MiB allocated

Accuracy

Total -59.3b remaining (-4203.2%)

Threshold costs -59.3b (-4203.2%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-27.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	299
1	112	299

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps 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 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.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 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps 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 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (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)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))

soundness1.4s (9.4%)

Memory

22.1MiB live, 990.3MiB allocated

Rules

18 726×	`lower-fma.f64`
18 726×	`lower-fma.f32`
17 506×	`lower-fma.f64`
17 506×	`lower-fma.f32`
16 678×	`lower-fma.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
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	375	5437
1	1220	5135
2	3564	5072
0	8239	4650
0	394	3903
1	1243	3731
2	3512	3683
0	8152	3378
0	425	5722
1	1335	5443
2	3800	5376
0	8393	4959

Stop Event

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

Compiler

Compiled 427 to 231 computations (45.9% saved)

preprocess119.0ms (0.8%)

Memory: -12.6MiB live, 301.8MiB allocated
Compiler: Compiled 424 to 178 computations (58% 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

analyze60.0ms (0.4%)

sample6.2s (41.4%)

preprocess28.0ms (0.2%)

explain86.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize23.0ms (0.2%)

series42.0ms (0.3%)

simplify457.0ms (3.1%)

rewrite590.0ms (4%)

eval36.0ms (0.2%)

prune31.0ms (0.2%)

simplify450.0ms (3%)

localize128.0ms (0.9%)

series32.0ms (0.2%)

simplify411.0ms (2.8%)

rewrite348.0ms (2.3%)

eval125.0ms (0.8%)

prune137.0ms (0.9%)

simplify666.0ms (4.5%)

localize182.0ms (1.2%)

series16.0ms (0.1%)

simplify504.0ms (3.4%)

rewrite308.0ms (2.1%)

eval231.0ms (1.5%)

prune101.0ms (0.7%)

simplify334.0ms (2.2%)

localize231.0ms (1.6%)

series73.0ms (0.5%)

simplify374.0ms (2.5%)

rewrite399.0ms (2.7%)

eval250.0ms (1.7%)

prune277.0ms (1.9%)

regimes63.0ms (0.4%)

regimes24.0ms (0.2%)

regimes33.0ms (0.2%)

regimes19.0ms (0.1%)

regimes26.0ms (0.2%)

regimes18.0ms (0.1%)

regimes27.0ms (0.2%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes24.0ms (0.2%)

regimes7.0ms (0%)

regimes6.0ms (0%)

simplify10.0ms (0.1%)

soundness1.4s (9.4%)

preprocess119.0ms (0.8%)

end0.0ms (0%)

Profiling

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

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