Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze43.0ms (0.3%)

Memory

-10.7MiB live, 69.9MiB 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)

sample6.4s (44.7%)

Memory

-122.1MiB live, 6 529.6MiB allocated

Samples

3.3s	25 804×	0	invalid
699.0ms	2 821×	1	valid
647.0ms	5 435×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

const: 886.0ms (28.1% of total)

ival-sin: 624.0ms (19.8% of total)

ival-fabs: 331.0ms (10.5% of total)

ival-mult: 238.0ms (7.6% of total)

ival-<: 227.0ms (7.2% of total)

ival-add: 226.0ms (7.2% of total)

ival-<=: 223.0ms (7.1% of total)

ival-sub: 176.0ms (5.6% of total)

ival-and: 94.0ms (3% of total)

adjust: 71.0ms (2.3% of total)

exact: 42.0ms (1.3% of total)

ival-assert: 11.0ms (0.3% of total)

Bogosity

explain124.0ms (0.9%)

Memory

5.3MiB live, 124.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
220	2	(-1.8662976358927449e-93 9.753130905532037e-96)	-	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
3	0	-	-	`(sin.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(sin.f64 x)`
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	222	4
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	3	0

Confusion

	Predicted +	Predicted -
+	223	0
-	2	31

Precision

0.9911111111111112

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	223	0	0
-	2	4	27

Precision?

0.9737991266375546

Recall?

1.0

Freqs

test

number	freq
0	31
1	225

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	196×	1	valid
15.0ms	314×	0	valid
2.0ms	2×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sin: 11.0ms (52.6% of total)

adjust: 4.0ms (19.1% of total)

ival-add: 3.0ms (14.3% of total)

ival-sub: 3.0ms (14.3% of total)

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

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

preprocess52.0ms (0.4%)

Memory

2.9MiB live, 35.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

-17.9MiB live, 21.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sin.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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)

localize34.0ms (0.2%)

Memory

-6.3MiB live, 49.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.11960381926531669	(sin.f64 (+.f64 x eps))
accuracy	25.528728926354475	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

9.0ms	98×	1	valid
7.0ms	157×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 5.0ms (48.1% of total)

adjust: 2.0ms (19.2% of total)

ival-add: 2.0ms (19.2% of total)

ival-sub: 2.0ms (19.2% of total)

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

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

series4.0ms (0%)

Memory

10.3MiB live, 10.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify259.0ms (1.8%)

Memory

-6.0MiB live, 384.9MiB 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)

rewrite267.0ms (1.9%)

Memory

-53.0MiB live, 425.3MiB allocated

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 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (.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 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) #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 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.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 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))))) #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))

eval35.0ms (0.2%)

Memory: 13.6MiB live, 50.3MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune45.0ms (0.3%)

Memory

-15.4MiB live, 66.7MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	275	16	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	275	17	292

Accuracy

100.0%

Counts

292 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.3%	(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)))
▶	60.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	9.4%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
	32.4%	(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
▶	32.3%	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	58.3%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
	58.1%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	7.7%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
	99.6%	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
▶	99.8%	(.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))
	58.7%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
	58.5%	#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 559 to 338 computations (39.5% saved)

simplify137.0ms (1%)

Memory

10.6MiB live, 168.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))
cost-diff	0	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
cost-diff	14528	(.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))))
cost-diff	0	(sin.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (+ x eps)) (sin.f64 eps))
cost-diff	0	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.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

3 866×	`lower-*.f32`
3 852×	`lower-*.f64`
2 580×	`lower-fma.f32`
2 576×	`lower-fma.f64`
1 554×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	207
0	63	173
1	94	173
2	161	173
3	249	169
4	439	169
5	1137	169
6	2813	169
7	4893	169
8	6750	169
0	8095	164

Stop Event

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

Calls

Call 1

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

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

localize118.0ms (0.8%)

Memory

9.4MiB live, 123.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 eps)
accuracy	0.015625	(*.f64 (cos.f64 x) (sin.f64 eps))
accuracy	0.03191376953688403	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
accuracy	25.530588745532118	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
accuracy	0.1388513381984477	(sin.f64 (-.f64 x eps))
accuracy	0.22265625	(/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))
accuracy	25.528728926354475	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
accuracy	32.19134806375718	(.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))))
accuracy	0	(sin.f64 x)
accuracy	0	(sin.f64 eps)
accuracy	25.528728926354475	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
accuracy	58.699629887603685	#s(approx (sin (+ x eps)) (sin.f64 eps))
accuracy	0	(sin.f64 eps)
accuracy	1.6212958519002514	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.00390625	(.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	0.00390625	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.01171875	(.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	0.13787929862874887	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

41.0ms	102×	1	valid
32.0ms	149×	0	valid
3.0ms	3×	3	valid
2.0ms	2×	2	valid

Compiler

Compiled 206 to 34 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 14.0ms (24.9% of total)

ival-sin: 12.0ms (21.4% of total)

adjust: 8.0ms (14.2% of total)

ival-cos: 8.0ms (14.2% of total)

ival-sub: 6.0ms (10.7% of total)

ival-add: 5.0ms (8.9% of total)

ival-div: 3.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series41.0ms (0.3%)

Memory

-10.7MiB live, 33.9MiB allocated

Counts

21 → 444

Calls

Call 1

Inputs
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))>
#<alt #s(approx (sin (+ x eps)) (sin.f64 eps))>
#<alt (sin.f64 x)>
#<alt (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))))>
#<alt (-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))>
#<alt (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))>
#<alt (sin.f64 (+.f64 x eps))>
#<alt (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))>
#<alt (cos.f64 eps)>
#<alt (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>
#<alt (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))>
#<alt (sin.f64 (-.f64 x eps))>
#<alt (*.f64 (cos.f64 x) (sin.f64 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>
#<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 (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 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 (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 (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) (sin (neg eps)))>
#<alt (+ (* x (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps)))) (* (sin eps) (sin (neg eps))))>
#<alt (+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (* (cos eps) (cos (neg eps))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps))))>
#<alt (+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (+ (* x (+ (* -1/2 (* (cos eps) (sin (neg eps)))) (+ (* -1/2 (* (cos (neg eps)) (sin eps))) (+ (* -1/6 (* (cos eps) (sin (neg eps)))) (* -1/6 (* (cos (neg eps)) (sin eps))))))) (* (cos eps) (cos (neg eps)))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps))))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x))))>
#<alt (* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x))))>
#<alt (* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x))))>
#<alt (* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x))))>
#<alt (pow (sin x) 2)>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (sin x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (* -1 (pow (sin x) 2)))) (* (cos x) (sin x))))) (pow (sin x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (+ (* -1 (pow (sin x) 2)) (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* -1/6 (* (cos x) (sin x))) (+ (* 1/6 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x)))))))))) (* (cos x) (sin x))))) (pow (sin x) 2))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ eps x)) (sin (- x eps)))>
#<alt (* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps))))>
#<alt (* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps))))>
#<alt (* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps))))>
#<alt (* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps))))>
#<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 (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 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin 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)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* -1 x))>
#<alt (+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))>
#<alt (+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (cos x)) (sin x))>
#<alt (- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))>
#<alt (- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (/ 1 (sin (neg eps)))>
#<alt (+ (* -1 (/ (* x (cos (neg eps))) (pow (sin (neg eps)) 2))) (/ 1 (sin (neg eps))))>
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps))))>
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (+ (* 1/2 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (/ (* (cos (neg eps)) (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (sin (neg eps))))))) (* 1/2 (/ 1 (sin (neg eps))))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps))))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (neg (+ eps (* -1 x)))))>
#<alt (/ 1 (sin (neg (+ eps (* -1 x)))))>
#<alt (/ 1 (sin (neg (+ eps (* -1 x)))))>
#<alt (/ 1 (sin (neg (+ eps (* -1 x)))))>
#<alt (/ 1 (sin x))>
#<alt (+ (/ 1 (sin x)) (/ (* eps (cos x)) (pow (sin x) 2)))>
#<alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))>
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x))) (+ (* -1/2 (/ (cos x) (pow (sin x) 2))) (* 1/6 (/ (cos x) (pow (sin x) 2))))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (- x eps)))>
#<alt (/ 1 (sin (+ x (* -1 eps))))>
#<alt (/ 1 (sin (+ x (* -1 eps))))>
#<alt (/ 1 (sin (+ x (* -1 eps))))>
#<alt (/ 1 (sin (+ x (* -1 eps))))>
#<alt (sin (neg eps))>
#<alt (+ (sin (neg eps)) (* x (cos (neg eps))))>
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps)))))))>
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps)))))))))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* -1 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x))))))))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>

Calls

111 calls:

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

simplify259.0ms (1.8%)

Memory

32.2MiB live, 254.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 712×	`lower-fma.f64`
10 712×	`lower-fma.f32`
6 704×	`lower-*.f64`
6 704×	`lower-*.f32`
3 266×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	4259
1	1534	4009
2	4407	3950
0	8345	3693

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 427

Calls

Call 1

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

rewrite302.0ms (2.1%)

Memory

19.1MiB live, 290.4MiB allocated

Rules

4 876×	`lower-*.f32`
4 862×	`lower-*.f64`
4 448×	`lower-/.f32`
4 446×	`lower-/.f64`
3 090×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	169
0	63	151
1	216	135
2	1789	135
0	8756	135

Stop Event

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

Counts

21 → 452

Calls

Call 1

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

eval164.0ms (1.1%)

Memory: -15.2MiB live, 184.5MiB allocated
Compiler: Compiled 25 479 to 2 307 computations (90.9% saved)

prune104.0ms (0.7%)

Memory

-8.0MiB live, 185.6MiB allocated

Pruning

20 alts after pruning (15 fresh and 5 done)

	Pruned	Kept	Total
New	1 008	10	1 018
Fresh	6	5	11
Picked	1	4	5
Done	0	1	1
Total	1 015	20	1 035

Accuracy

100.0%

Counts

1 035 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
✓	32.3%	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	58.1%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
✓	7.7%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
	7.7%	(-.f64 #s(approx (sin (+ x eps)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps))) (sin.f64 x))
	99.6%	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	59.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.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)))))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.7%	(.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))
	58.7%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
	98.2%	#s(approx (- (* (* (sin (+ x eps)) (sin (- x eps))) (/ 1 (sin (- x eps)))) (sin x)) (*.f64 eps (cos.f64 x)))
▶	58.5%	#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
▶	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 628 to 379 computations (39.6% saved)

simplify301.0ms (2.1%)

Memory

21.3MiB live, 253.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
cost-diff	0	(-.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)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
cost-diff	0	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
cost-diff	0	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.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)))))) #s(literal 2 binary64))
cost-diff	128	(-.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)))))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

9 638×	`lower-fma.f32`
9 626×	`lower-fma.f64`
4 500×	`lower-*.f32`
4 464×	`lower-*.f64`
1 636×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	432
0	105	394
1	173	360
2	344	357
3	854	357
4	1533	357
5	2353	357
6	3664	357
7	4648	357
8	6046	357
9	6670	357
10	6753	357
11	6776	357
12	6870	357
13	7045	357
14	7531	357
15	7840	357
0	8008	344

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

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

localize213.0ms (1.5%)

Memory

-9.7MiB live, 355.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
accuracy	0.015625	(*.f64 x (cos.f64 eps))
accuracy	1.3953154985182241	#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
accuracy	25.52340800606589	(-.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)
accuracy	0.01171875	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.13787929862874887	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.3203125	(*.f64 eps #s(literal -1/48 binary64))
accuracy	0.7121935378069335	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.05859375	(.f64 x (.f64 x x))
accuracy	0.11960381926531669	(sin.f64 (+.f64 x eps))
accuracy	1.3671294627560198	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	25.528728926354475	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
accuracy	0	(*.f64 eps eps)
accuracy	0.1875	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
accuracy	0.8068948319168083	#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
accuracy	1.6212958519002514	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
accuracy	0.01171875	(-.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)))))
accuracy	0.01171875	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.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))))))
accuracy	0.015625	(.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01953125	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

71.0ms	98×	1	valid
67.0ms	156×	0	valid
4.0ms	2×	3	valid

Compiler

Compiled 366 to 56 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 41.0ms (36.9% of total)

ival-sin: 24.0ms (21.6% of total)

ival-add: 14.0ms (12.6% of total)

adjust: 10.0ms (9% of total)

ival-cos: 10.0ms (9% of total)

const: 7.0ms (6.3% of total)

ival-sub: 4.0ms (3.6% of total)

exact: 1.0ms (0.9% of total)

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

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

series31.0ms (0.2%)

Memory

3.7MiB live, 42.1MiB allocated

Counts

28 → 540

Calls

Call 1

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

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<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 (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin 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 eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (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))>
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#<alt x>
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#<alt (sin x)>
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#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
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#<alt x>
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#<alt x>
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#<alt (* eps (cos x))>
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#<alt 1>
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#<alt (* (cos x) (cos (* 1/2 eps)))>
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#<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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
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#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt x>
#<alt (+ x (* -1/2 (* (pow eps 2) x)))>
#<alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))))>
#<alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x))))))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>
#<alt (* x (cos eps))>

Calls

135 calls:

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

simplify322.0ms (2.3%)

Memory

29.5MiB live, 328.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 156×	`lower-fma.f64`
13 156×	`lower-fma.f32`
6 954×	`lower-*.f64`
6 954×	`lower-*.f32`
4 284×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	437	5459
1	1398	5239
2	4053	5170
0	8383	4850

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 502

Calls

Call 1

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

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)))
(+ (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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #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 x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 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 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.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 x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
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(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(.f64 (cos.f64 x) (+.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 binary64)))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 (*.f64 eps eps) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (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 (*.f64 eps (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))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.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 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.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 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 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)
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(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 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)))
(+ (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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #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 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.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))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
x
(+ x (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 eps eps) (.f64 x #s(literal -1/2 binary64)) x)
(+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))))
(fma.f64 (.f64 x (.f64 eps eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x))))))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 x (.f64 eps eps)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x #s(literal -1/2 binary64))) x)
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))
(* x (cos eps))
(*.f64 x (cos.f64 eps))

rewrite306.0ms (2.1%)

Memory

-44.4MiB live, 341.6MiB allocated

Rules

4 408×	`lower-*.f32`
4 372×	`lower-*.f64`
4 098×	`lower-fma.f32`
4 086×	`lower-fma.f64`
3 790×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	340
0	105	316
1	326	252
2	2508	252
0	8379	242

Stop Event

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

Counts

28 → 652

Calls

Call 1

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

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

eval149.0ms (1%)

Memory: 41.9MiB live, 273.6MiB allocated
Compiler: Compiled 32 458 to 2 762 computations (91.5% saved)

prune172.0ms (1.2%)

Memory

-43.1MiB live, 245.9MiB allocated

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	1 151	16	1 167
Fresh	3	7	10
Picked	5	0	5
Done	0	5	5
Total	1 159	28	1 187

Accuracy

100.0%

Counts

1 187 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
✓	32.3%	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.7%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.6%	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	59.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 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)))))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 (cos.f64 (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))))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 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))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps)))))) #s(literal 2 binary64))
	98.1%	(.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)))) #s(approx (cos (* (+ (* x 2) eps) 1/2)) (cos.f64 x))) #s(literal 2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 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))
	58.7%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
	98.2%	#s(approx (- (* (* (sin (+ x eps)) (sin (- x eps))) (/ 1 (sin (- x eps)))) (sin x)) (*.f64 eps (cos.f64 x)))
	58.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 x eps) #s(literal 1 binary64)) x)) x))
	58.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)))
▶	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps #s(literal -1/6 binary64)) eps)))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (+.f64 (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) eps)))
▶	5.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))))

Compiler

Compiled 910 to 531 computations (41.6% saved)

simplify267.0ms (1.9%)

Memory

44.5MiB live, 273.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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))
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))
cost-diff	0	(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)))
cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
cost-diff	0	(.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)))
cost-diff	0	#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))
cost-diff	0	#s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) (sin.f64 eps))
cost-diff	128	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))

Rules

17 096×	`lower-fma.f32`
17 080×	`lower-fma.f64`
4 552×	`lower-*.f32`
4 524×	`lower-*.f64`
2 322×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	519
0	109	503
1	206	497
2	550	495
3	1532	487
4	2677	487
5	4379	487
6	6214	487
0	8151	471

Stop Event

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

Calls

Call 1

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

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

localize415.0ms (2.9%)

Memory

-24.9MiB live, 501.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(.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))))
accuracy	0.13787929862874887	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.3203125	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
accuracy	0.6423238934052802	#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	0.12109375	(.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
accuracy	0.31640625	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
accuracy	0.8307837210457609	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps))
accuracy	1.3953154985182241	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
accuracy	0.01171875	(.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)))
accuracy	0.109375	(*.f64 x (+.f64 x eps))
accuracy	0.8295860775012747	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps))
accuracy	1.3953154985182241	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
accuracy	0.1484375	(.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)))
accuracy	0.8068948319168083	#s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps)))))
accuracy	1.6212958519002514	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))))
accuracy	60.283753180483394	#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))
accuracy	0	(cos.f64 eps)
accuracy	0.01171875	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
accuracy	0.015625	(*.f64 (cos.f64 x) (sin.f64 eps))
accuracy	17.846866166555525	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))

Samples

240.0ms	227×	1	valid
22.0ms	17×	2	valid
5.0ms	11×	0	valid
3.0ms	1×	3	valid

Compiler

Compiled 354 to 66 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 223.0ms

ival-mult: 69.0ms (31% of total)

ival-add: 53.0ms (23.8% of total)

adjust: 37.0ms (16.6% of total)

ival-sin: 23.0ms (10.3% of total)

const: 22.0ms (9.9% of total)

ival-cos: 12.0ms (5.4% of total)

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

exact: 1.0ms (0.4% of total)

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

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

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

series25.0ms (0.2%)

Memory

13.5MiB live, 51.2MiB allocated

Counts

26 → 540

Calls

Call 1

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

Outputs
#<alt (* x (- (cos eps) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (* -1 x)) (* (cos eps) (sin x)))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (+ (sin (neg x)) (* (cos eps) (sin x)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin x) (sin (neg x)))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (cos x))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))>
#<alt (+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1/6 (pow eps 3))>
#<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) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (* -1/2 (* (pow x 2) (sin eps)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))>
#<alt (* -1/2 (* (pow x 2) (sin eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin 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 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<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 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 (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 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 (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) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (* -1/2 (* (pow x 2) (sin eps)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))>
#<alt (* -1/2 (* (pow x 2) (sin eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin eps))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (+ (* -1 (cos eps)) (* -1 (/ (sin eps) x)))) x)) (* -1/2 (sin 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 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (+ (* -1/6 (+ 1 (* -1/2 (pow x 2)))) (* 1/24 (* eps x)))))))))>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<alt (- (+ (* x (cos eps)) (* (sin eps) (+ 1 (* -1/2 (pow x 2))))) x)>
#<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 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))>
#<alt (* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)))))>
#<alt (+ eps (* -1/6 (pow eps 3)))>
#<alt (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))>
#<alt (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))>
#<alt (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* -1/6 (/ (pow eps 3) (pow x 2))) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* -1/6 (/ (pow eps 3) (pow x 2))) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ eps (pow x 2))))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))>
#<alt (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))>
#<alt (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))>
#<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 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* eps x)>
#<alt (* x (+ eps x))>
#<alt (* x (+ eps x))>
#<alt (* x (+ eps x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (pow x 2)>
#<alt (+ (* eps x) (pow x 2))>
#<alt (+ (* eps x) (pow x 2))>
#<alt (+ (* eps x) (pow x 2))>
#<alt (* eps x)>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps x)>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* -1/6 eps)>
#<alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))>
#<alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))>
#<alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<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))))>

Calls

135 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps)
1.0ms	eps	@	inf	(+ (* eps (* -1/2 (* x (+ x eps)))) eps)
1.0ms	eps	@	-inf	(+ (* eps (* -1/2 (* x (+ x eps)))) eps)
1.0ms	eps	@	0	(+ (* eps (* -1/2 (* x (+ x eps)))) eps)
0.0ms	eps	@	-inf	(+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps)

simplify307.0ms (2.1%)

Memory

7.0MiB live, 363.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 788×	`lower-fma.f64`
11 788×	`lower-fma.f32`
7 516×	`lower-*.f64`
7 516×	`lower-*.f32`
2 610×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	578	6254
1	1796	6002
2	5289	5961
0	8059	5503

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 534

Calls

Call 1

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

Outputs
(* x (- (cos eps) 1))
(-.f64 (*.f64 x (cos.f64 eps)) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(-.f64 (.f64 x (fma.f64 x (.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64))) (cos.f64 eps))) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(.f64 x (+.f64 (cos.f64 eps) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (cos.f64 eps) #s(literal 1/120 binary64) #s(literal -1/120 binary64))) (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (cos.f64 eps) #s(literal -1/5040 binary64) #s(literal 1/5040 binary64)) (fma.f64 (cos.f64 eps) #s(literal 1/120 binary64) #s(literal -1/120 binary64))) #s(literal 1/6 binary64))) (cos.f64 eps)) (neg.f64 x))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (* -1 x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin x) (sin (neg x)))
#s(literal 0 binary64)
(+ (sin x) (+ (sin (neg x)) (* -1/2 (* (pow eps 2) (sin x)))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* (cos eps) (sin x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)) (+.f64 (cos.f64 eps) #s(literal -1 binary64))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 eps) (*.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)))) (+.f64 (cos.f64 eps) #s(literal -1 binary64))) (sin.f64 eps))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (* -1 x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin x) (sin (neg x)))
#s(literal 0 binary64)
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(fma.f64 eps (cos.f64 x) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) #s(literal 0 binary64))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(fma.f64 (.f64 x x) (.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 eps))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(fma.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (sin.f64 eps) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (*.f64 x x))))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
(* (cos x) (sin eps))
(*.f64 (sin.f64 eps) (cos.f64 x))
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(fma.f64 x (-.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #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 (fma.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))) (.f64 x #s(literal 1/6 binary64)))) (neg.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))))
(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 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/8 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (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 (fma.f64 (cos.f64 x) #s(literal -1/8 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 (sin.f64 x) #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))

rewrite496.0ms (3.5%)

Memory

21.7MiB live, 527.3MiB allocated

Rules

7 126×	`lower-*.f32`
7 098×	`lower-*.f64`
6 766×	`lower-fma.f32`
6 750×	`lower-fma.f64`
4 072×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	427
0	109	413
1	402	400
2	3620	400
0	10628	389

Stop Event

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

Counts

26 → 919

Calls

Call 1

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

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

eval402.0ms (2.8%)

Memory: 9.2MiB live, 307.4MiB allocated
Compiler: Compiled 65 856 to 3 636 computations (94.5% saved)

prune295.0ms (2.1%)

Memory

-9.4MiB live, 368.8MiB allocated

Pruning

32 alts after pruning (25 fresh and 7 done)

	Pruned	Kept	Total
New	1 478	14	1 492
Fresh	7	11	18
Picked	3	2	5
Done	0	5	5
Total	1 488	32	1 520

Accuracy

100.0%

Counts

1 520 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.1%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
✓	32.3%	(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.7%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
✓	99.6%	(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	98.9%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
	98.7%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))))
	59.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 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)))))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 (cos.f64 (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))))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 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 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	98.9%	(.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) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
	98.1%	(.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)))) #s(approx (cos (* (+ (* x 2) eps) 1/2)) (cos.f64 x))) #s(literal 2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 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))
	58.7%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
	98.2%	#s(approx (- (* (* (sin (+ x eps)) (sin (- x eps))) (/ 1 (sin (- x eps)))) (sin x)) (*.f64 eps (cos.f64 x)))
	58.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 x eps) #s(literal 1 binary64)) x)) x))
	58.4%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))))) eps)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (*.f64 eps #s(literal -1/6 binary64))))) eps)))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6)))) (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))))
	5.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))
	5.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
	6.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
	99.6%	#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 (neg.f64 x)))))
	5.7%	#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 1 501 to 558 computations (62.8% saved)

regimes53.0ms (0.4%)

Memory

2.7MiB live, 80.6MiB allocated

Counts

57 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (+.f64 (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 x eps) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6)))) (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (*.f64 eps #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (* (* (sin (+ x eps)) (sin (- x eps))) (/ 1 (sin (- x eps)))) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.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 #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 #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #s(approx (cos (* (+ (* x 2) eps) 1/2)) (cos.f64 x))) #s(literal 2 binary64))
(-.f64 #s(approx (sin (+ x eps)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps))) (sin.f64 x))
(.f64 (.f64 (cos.f64 (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))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 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 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (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 (.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 (.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) (*.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 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
(-.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))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
(.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 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps)))))) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
(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)))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 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)))))) #s(literal 2 binary64))
#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (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 (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 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.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)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))

Outputs

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

Calls

3 calls:

18.0ms	eps
17.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes54.0ms (0.4%)

Memory

-3.9MiB live, 76.7MiB allocated

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* -1/2 (* x (+ x eps)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps #s(literal -1/6 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (+.f64 (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 x eps) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6)))) (fma.f64 x (.f64 eps #s(literal -1/2 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (*.f64 eps #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (+ (* -1/2 (* x (+ x eps))) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))) eps) (fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 x eps)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (* (* (sin (+ x eps)) (sin (- x eps))) (/ 1 (sin (- x eps)))) (sin x)) (*.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.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 #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 #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #s(approx (cos (* (+ (* x 2) eps) 1/2)) (cos.f64 x))) #s(literal 2 binary64))
(-.f64 #s(approx (sin (+ x eps)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps))) (sin.f64 x))
(.f64 (.f64 (cos.f64 (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))))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 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 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (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 (.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 (.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) (*.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 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
(-.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))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.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))
(.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 (.f64 (sin.f64 (.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) eps)))))) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) (sin.f64 x))
(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)))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 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)))))) #s(literal 2 binary64))
#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (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 (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))))

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))

Calls

3 calls:

20.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
17.0ms	eps
14.0ms	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)

regimes45.0ms (0.3%)

Memory

-18.5MiB live, 60.0MiB allocated

Counts

41 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

18.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	x
11.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.3%)

Memory

27.4MiB live, 66.7MiB allocated

Counts

36 → 1

Calls

Call 1

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

Calls

3 calls:

14.0ms	x
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory

-30.3MiB live, 89.6MiB allocated

Counts

35 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

22.8MiB live, 61.6MiB allocated

Counts

32 → 1

Calls

Call 1

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x
9.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

-19.0MiB live, 60.7MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs
(.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))

Calls

3 calls:

10.0ms	eps
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes68.0ms (0.5%)

Memory

7.5MiB live, 45.2MiB allocated

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

51.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x
7.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.2%)

Memory

-12.6MiB live, 26.9MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

37.1MiB live, 37.1MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory

-19.3MiB live, 22.7MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes19.0ms (0.1%)

Memory

-3.5MiB live, 34.8MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	eps
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	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)

regimes13.0ms (0.1%)

Memory

-14.1MiB live, 25.2MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.0%	1	`x`
6.0%	1	`eps`
6.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

10.4MiB live, 10.4MiB allocated

Accuracy

Total -0.2b remaining (-0.3%)

Threshold costs -0.2b (-0.3%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

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

Outputs
#s(approx (+ (* (cos x) (sin eps)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.7%	1	`eps`
5.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
5.7%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify15.0ms (0.1%)

Memory

-20.1MiB live, 19.3MiB allocated

Algorithm

1×	egg-herbie

Rules

88×	`*-commutative_binary64`
14×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	512
1	204	512
2	215	512
3	221	512
4	225	512
5	226	512

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (11.1%)

Memory

14.4MiB live, 1 414.1MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
13 156×	`lower-fma.f64`
13 156×	`lower-fma.f32`
11 788×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	4259
1	1534	4009
2	4407	3950
0	8345	3693
0	61	340
0	105	316
1	326	252
2	2508	252
0	8379	242
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	36	169
0	63	151
1	216	135
2	1789	135
0	8756	135
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	578	6254
1	1796	6002
2	5289	5961
0	8059	5503
0	437	5459
1	1398	5239
2	4053	5170
0	8383	4850

Stop Event

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

Compiler

Compiled 644 to 342 computations (46.9% saved)

preprocess135.0ms (0.9%)

Memory: 16.3MiB live, 242.2MiB allocated
Compiler: Compiled 644 to 250 computations (61.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze43.0ms (0.3%)

sample6.4s (44.7%)

explain124.0ms (0.9%)

preprocess52.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize34.0ms (0.2%)

series4.0ms (0%)

simplify259.0ms (1.8%)

rewrite267.0ms (1.9%)

eval35.0ms (0.2%)

prune45.0ms (0.3%)

simplify137.0ms (1%)

localize118.0ms (0.8%)

series41.0ms (0.3%)

simplify259.0ms (1.8%)

rewrite302.0ms (2.1%)

eval164.0ms (1.1%)

prune104.0ms (0.7%)

simplify301.0ms (2.1%)

localize213.0ms (1.5%)

series31.0ms (0.2%)

simplify322.0ms (2.3%)

rewrite306.0ms (2.1%)

eval149.0ms (1%)

prune172.0ms (1.2%)

simplify267.0ms (1.9%)

localize415.0ms (2.9%)

series25.0ms (0.2%)

simplify307.0ms (2.1%)

rewrite496.0ms (3.5%)

eval402.0ms (2.8%)

prune295.0ms (2.1%)

regimes53.0ms (0.4%)

regimes54.0ms (0.4%)

regimes45.0ms (0.3%)

regimes36.0ms (0.3%)

regimes34.0ms (0.2%)

regimes29.0ms (0.2%)

regimes29.0ms (0.2%)

regimes68.0ms (0.5%)

regimes23.0ms (0.2%)

regimes19.0ms (0.1%)

regimes22.0ms (0.2%)

regimes19.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0%)

regimes5.0ms (0%)

simplify15.0ms (0.1%)

soundness1.6s (11.1%)

preprocess135.0ms (0.9%)

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