Metrics for 2sin (example 3.3)

analyze77.0ms (0.5%)

Memory

-29.8MiB live, 62.7MiB 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)

sample6.5s (44.3%)

Memory

-196.5MiB live, 8 937.4MiB allocated

Samples

3.3s	25 620×	0	invalid
1.0s	4 430×	1	valid
814.0ms	3 826×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.9s

const: 1.0s (25.8% of total)

ival-sin: 851.0ms (21.7% of total)

ival-<=: 354.0ms (9% of total)

ival-fabs: 340.0ms (8.7% of total)

ival-add: 335.0ms (8.6% of total)

ival-mult: 302.0ms (7.7% of total)

ival-<: 245.0ms (6.3% of total)

ival-sub: 238.0ms (6.1% of total)

ival-and: 99.0ms (2.5% of total)

adjust: 84.0ms (2.1% of total)

exact: 44.0ms (1.1% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

preprocess27.0ms (0.2%)

Memory

-8.7MiB live, 29.9MiB allocated

Algorithm

2×	egg-herbie

Rules

114×	`sub-neg`
80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
76×	`cancel-sign-sub-inv`
62×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(- (sin (+ x (neg eps))) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(neg (- (sin (+ x (neg eps))) (sin x)))
(- (sin (+ eps x)) (sin eps))

Outputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ x (neg eps))) (sin x))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ x (neg eps))) (sin x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ eps x)) (sin eps))
(- (sin (+ x eps)) (sin eps))

explain88.0ms (0.6%)

Memory

18.4MiB live, 138.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
233	-	2	(2.270818488837445e-212 3.5723729624353062e-214)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	-	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	231	8

Confusion

	Predicted +	Predicted -
+	231	2
-	0	23

Precision

1.0

Recall

0.9914163090128756

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	231	2	0
-	0	6	17

Precision?

0.9748953974895398

Recall?

1.0

Freqs

test

number	freq
0	25
1	231

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms	274×	1	valid
11.0ms	234×	0	valid
1.0ms	4×	2	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-sin: 10.0ms (47.5% of total)

ival-add: 4.0ms (19% of total)

adjust: 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)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
48×	`-lowering-.f32`
48×	`-lowering-.f64`
36×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize46.0ms (0.3%)

Memory

-16.8MiB live, 21.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

33.0ms	137×	1	valid
5.0ms	117×	0	valid
0.0ms	2×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-add: 22.0ms (71.6% of total)

ival-sin: 5.0ms (16.3% of total)

adjust: 2.0ms (6.5% of total)

ival-sub: 2.0ms (6.5% of total)

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

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

series4.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite328.0ms (2.2%)

Memory

-6.2MiB live, 426.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 986×	`accelerator-lowering-fma.f32`
4 986×	`accelerator-lowering-fma.f64`
4 676×	`-lowering-.f32`
4 676×	`-lowering-.f64`
2 176×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	49	16
2	376	16
3	4763	16
0	8212	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 214

Calls

Call 1

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

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

simplify440.0ms (3%)

Memory

0.9MiB live, 671.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
4 132×	`-lowering-.f32`
4 132×	`-lowering-.f64`
2 614×	`+-lowering-+.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 → 84

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

eval52.0ms (0.3%)

Memory: -21.5MiB live, 54.7MiB allocated
Compiler: Compiled 8 005 to 859 computations (89.3% saved)

prune34.0ms (0.2%)

Memory

-12.1MiB live, 68.6MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	292	6	298
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	6	299

Accuracy

100.0%

Counts

299 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.9%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
▶	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
▶	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
▶	99.7%	(*.f64 eps (cos.f64 x))
▶	98.5%	(sin.f64 eps)

Compiler

Compiled 184 to 122 computations (33.7% saved)

simplify453.0ms (3.1%)

Memory

18.2MiB live, 607.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

17 474×	`accelerator-lowering-fma.f32`
17 474×	`accelerator-lowering-fma.f64`
2 980×	`-lowering-.f32`
2 980×	`-lowering-.f64`
2 374×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	304
1	105	304
2	326	296
3	922	296
4	2586	296
5	4665	296
6	5769	296
7	6794	296
8	7186	288
9	7276	288
10	7638	288
0	8047	263

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
(sin eps)
eps
(* eps (cos x))
eps
(cos x)
x
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))
(+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))
1
(* (* x x) (+ -1/6 (* (* x x) 1/120)))
(* x x)
(+ -1/6 (* (* x x) 1/120))
-1/6
(* (* x x) 1/120)
1/120
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))
1
(* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))
(* x x)
(+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))
-1/6
(* x (* x (+ 1/120 (* (* x x) -1/5040))))
(* x (+ 1/120 (* (* x x) -1/5040)))
(+ 1/120 (* (* x x) -1/5040))
1/120
(* (* x x) -1/5040)
-1/5040

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

localize212.0ms (1.4%)

Memory

14.9MiB live, 246.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/5040 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))))
✓	accuracy	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/120 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
✓	accuracy	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))

Samples

111.0ms	137×	1	valid
35.0ms	116×	0	valid
1.0ms	2×	2	valid
1.0ms	1×	3	valid

Compiler

Compiled 316 to 40 computations (87.3% saved)

Precisions

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

ival-mult: 26.0ms (31.1% of total)

const: 16.0ms (19.1% of total)

ival-add: 15.0ms (17.9% of total)

adjust: 7.0ms (8.4% of total)

ival-sin: 7.0ms (8.4% of total)

ival-div: 5.0ms (6% of total)

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

ival-sub: 3.0ms (3.6% of total)

exact: 1.0ms (1.2% of total)

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

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

series29.0ms (0.2%)

Memory

13.9MiB live, 51.8MiB allocated

Counts

20 → 348

Calls

Call 1

Inputs
#<alt (+ eps 0)>
#<alt (/ (+ eps (* x 2)) 2)>
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (sin eps)>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* (* x x) (+ -1/6 (* (* x x) 1/120)))>
#<alt (* (* x x) 1/120)>
#<alt (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))>
#<alt (* (* x x) -1/5040)>
#<alt (* x (+ 1/120 (* (* x x) -1/5040)))>

Outputs
#<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 x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt 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 (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* -1/120 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* -1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<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) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<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 (* -1/5040 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<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 (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 (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 (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))>
#<alt (* -1/5040 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* 1/120 x)>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>

Calls

87 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))))
2.0ms	x	@	inf	(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
1.0ms	x	@	0	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	x	@	inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	inf	(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))

rewrite452.0ms (3.1%)

Memory

-11.8MiB live, 584.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 998×	`-lowering-.f32`
4 998×	`-lowering-.f64`
3 940×	`/-lowering-/.f32`
3 940×	`/-lowering-/.f64`
3 024×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	192
1	248	184
2	2373	184
0	8454	166

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 435

Calls

Call 1

Inputs
(+ eps 0)
(/ (+ eps (* x 2)) 2)
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin eps)
(* eps (cos x))
(cos x)
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))))
(sin (+ x eps))
(+ x eps)
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))
(sin (/ (+ eps 0) 2))
(cos (/ (+ eps (* x 2)) 2))
(* (* x x) (+ -1/6 (* (* x x) 1/120)))
(* (* x x) 1/120)
(* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))
(* (* x x) -1/5040)
(* x (+ 1/120 (* (* x x) -1/5040)))

Outputs
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 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) 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 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps 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 eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (.f64 (-.f64 #s(literal 0 binary64) 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 (-.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 (neg.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (neg.f64 (.f64 eps (.f64 eps eps)))) (neg.f64 (neg.f64 (*.f64 eps 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))
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(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))))
(.f64 (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))) (.f64 x x))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64))))))) x)
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64))))))) (*.f64 x x))
(.f64 x (.f64 x #s(literal -1/5040 binary64)))
(.f64 (.f64 x x) #s(literal -1/5040 binary64))
(.f64 #s(literal -1/5040 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/5040 binary64)) x)
(+.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64)))
(fma.f64 x #s(literal 1/120 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/5040 binary64)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 #s(literal 1/120 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(fma.f64 #s(literal -1/5040 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) x (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/5040 binary64) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x #s(literal -1/5040 binary64)) (.f64 x x) (*.f64 x #s(literal 1/120 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64)))) (+.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))))) (-.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64)))) (+.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64)))) (-.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64))) x) (+.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64))) x) (-.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64))))) (neg.f64 (+.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64))))) (neg.f64 (-.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/128024064000 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64))) x)) (neg.f64 (-.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))
(.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(.f64 (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64))) x)

simplify428.0ms (2.9%)

Memory

10.8MiB live, 611.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 624×	`accelerator-lowering-fma.f32`
11 624×	`accelerator-lowering-fma.f64`
5 296×	`-lowering-.f32`
5 296×	`-lowering-.f64`
4 856×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	381	3514
1	1150	3346
2	3225	3310
0	8202	3062

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 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)))
(* 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)))
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 (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(* -1/120 (pow x 5))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(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) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(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)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/5040 (pow x 7))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
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))))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 7))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 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))
(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))))
(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))))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* -1/5040 (pow x 6))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 6))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))

Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
x
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps))) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+.f64 (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal -2 binary64))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal -2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 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 (+.f64 (.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 (+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.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))))
(+.f64 (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (+.f64 (.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))))))))
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(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
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(sin eps)
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(sin eps)
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(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
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(*.f64 eps (cos.f64 x))
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(* eps (cos x))
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(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
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(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
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(* eps (cos x))
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(* eps (cos x))
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(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (+.f64 (.f64 x (cos.f64 eps)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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(* -1/120 (pow x 5))
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(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (*.f64 x x))))) (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64)))))
(* -1/120 (pow x 5))
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(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
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(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (.f64 x (cos.f64 eps)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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(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)))
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(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)))
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
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(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 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(+ eps x)
(+.f64 eps x)
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(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
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(* eps (+ 1 (/ x eps)))
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(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))
(* 1/120 (pow x 5))
(*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
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(* 1/120 (pow x 5))
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(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
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(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))))
(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
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(* -1/5040 (pow x 2))
(.f64 #s(literal -1/5040 binary64) (.f64 x x))
(* -1/5040 (pow x 2))
(.f64 #s(literal -1/5040 binary64) (.f64 x x))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 x x))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 x x))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 x x))))
(* -1/5040 (pow x 3))
(.f64 #s(literal -1/5040 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* -1/5040 (pow x 3))
(.f64 #s(literal -1/5040 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 x (.f64 x x)))

eval134.0ms (0.9%)

Memory: 10.2MiB live, 200.4MiB allocated
Compiler: Compiled 31 538 to 2 280 computations (92.8% saved)

prune99.0ms (0.7%)

Memory

-25.8MiB live, 190.4MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	877	8	885
Fresh	0	1	1
Picked	5	0	5
Done	0	0	0
Total	882	9	891

Accuracy

100.0%

Counts

891 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.8%	(/.f64 (.f64 (.f64 eps eps) (cos.f64 x)) eps)
▶	99.7%	(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
▶	99.7%	(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
▶	100.0%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
	99.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
	99.5%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
▶	98.5%	eps

Compiler

Compiled 280 to 180 computations (35.7% saved)

simplify420.0ms (2.8%)

Memory

28.0MiB live, 586.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	128	(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
✓	cost-diff	256	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
✓	cost-diff	0	(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
✓	cost-diff	128	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
✓	cost-diff	0	(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	cost-diff	0	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))

Rules

9 176×	`accelerator-lowering-fma.f32`
9 176×	`accelerator-lowering-fma.f64`
7 280×	`-lowering-.f32`
7 280×	`-lowering-.f64`
6 242×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	305
1	103	299
2	348	297
3	939	291
4	1649	291
5	1875	291
6	1948	291
7	1951	275
8	1953	275
9	1976	275
10	2023	275
11	2124	275
12	2365	275
13	3073	275
14	5667	275
15	6574	275
16	6574	275
17	6574	275
18	6781	275
19	6907	275
20	7041	275
21	7078	275
22	7078	275
0	11372	247

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
1/2
(* -1/48 (* eps eps))
-1/48
(* eps eps)
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
eps
(+ eps (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x))))))
eps
(* (* x x) (* eps (+ -1/2 (* 1/24 (* x x)))))
(* x x)
x
(* eps (+ -1/2 (* 1/24 (* x x))))
(+ -1/2 (* 1/24 (* x x)))
-1/2
(* 1/24 (* x x))
1/24
(+ eps (* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))))
eps
(* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))))
(* x x)
x
(+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))
(* eps -1/2)
-1/2
(* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))
(* eps (* x x))
(+ 1/24 (* (* x x) -1/720))
1/24
(* (* x x) -1/720)
-1/720
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(* eps 1/2)
eps
1/2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2

Outputs
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps #s(literal 2 binary64))))
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))
1/2
#s(literal 1/2 binary64)
(* -1/48 (* eps eps))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
-1/48
#s(literal -1/48 binary64)
(* eps eps)
(*.f64 eps eps)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/ (+ eps (* x 2)) 2)
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
eps
(+ eps (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x))))))
(.f64 eps (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
eps
(* (* x x) (* eps (+ -1/2 (* 1/24 (* x x)))))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(* x x)
(*.f64 x x)
x
(* eps (+ -1/2 (* 1/24 (* x x))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(+ -1/2 (* 1/24 (* x x)))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
-1/2
#s(literal -1/2 binary64)
(* 1/24 (* x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(+ eps (* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))))
(.f64 eps (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) #s(literal 1 binary64)))
eps
(* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(* x x)
(*.f64 x x)
x
(+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))
(.f64 x (.f64 eps (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(* eps (* x x))
(.f64 eps (.f64 x x))
(+ 1/24 (* (* x x) -1/720))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
1/24
#s(literal 1/24 binary64)
(* (* x x) -1/720)
(.f64 (.f64 x x) #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 1/2 binary64)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/ (+ eps (* x 2)) 2)
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)

localize151.0ms (1%)

Memory

0.2MiB live, 192.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.9%	(.f64 eps (.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/720 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
✓	accuracy	99.7%	(.f64 #s(literal 1/24 binary64) (.f64 x x))
✓	accuracy	100.0%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	accuracy	100.0%	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.6%	(.f64 #s(literal -1/48 binary64) (.f64 eps eps))

Samples

94.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 307 to 37 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 24.0ms (49.1% of total)

const: 12.0ms (24.6% of total)

ival-add: 8.0ms (16.4% of total)

ival-div: 2.0ms (4.1% of total)

ival-cos: 2.0ms (4.1% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series43.0ms (0.3%)

Memory

11.9MiB live, 49.6MiB allocated

Counts

20 → 408

Calls

Call 1

Inputs
#<alt (/ (+ eps (* x 2)) 2)>
#<alt (* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* -1/48 (* eps eps))))>
#<alt (+ eps (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x))))))>
#<alt (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x)))))>
#<alt (* x x)>
#<alt (* eps (+ -1/2 (* 1/24 (* x x))))>
#<alt (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))>
#<alt (+ eps (* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))))>
#<alt (* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))))>
#<alt (* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps 1/2)>
#<alt (* -1/48 (* eps eps))>
#<alt (* 1/24 (* x x))>
#<alt (* (* x x) -1/720)>
#<alt (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))>
#<alt (* eps (* x x))>
#<alt (cos (/ (+ eps (* x 2)) 2))>

Outputs
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
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#<alt (* eps (cos x))>
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#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
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#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
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#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<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)) (* -1/16 (* eps (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))>
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (* 1/24 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))>
#<alt (* -1/720 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* -1/720 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<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 (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))))>

Calls

102 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	0	(+ eps (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x))))))
5.0ms	x	@	0	(+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))
2.0ms	eps	@	0	(+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))
1.0ms	x	@	inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite606.0ms (4.1%)

Memory

-24.0MiB live, 486.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 672×	`-lowering-.f32`
5 672×	`-lowering-.f64`
4 412×	`accelerator-lowering-fma.f32`
4 412×	`accelerator-lowering-fma.f64`
4 274×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	225
1	199	219
2	1678	219
0	8371	198

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 550

Calls

Call 1

Inputs
(/ (+ eps (* x 2)) 2)
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(+ eps (* (* x x) (* eps (+ -1/2 (* 1/24 (* x x))))))
(* (* x x) (* eps (+ -1/2 (* 1/24 (* x x)))))
(* x x)
(* eps (+ -1/2 (* 1/24 (* x x))))
(+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))
(+ eps (* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720))))))
(* (* x x) (+ (* eps -1/2) (* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))))
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(* eps 1/2)
(* -1/48 (* eps eps))
(* 1/24 (* x x))
(* (* x x) -1/720)
(* (* eps (* x x)) (+ 1/24 (* (* x x) -1/720)))
(* eps (* x x))
(cos (/ (+ eps (* x 2)) 2))

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

simplify637.0ms (4.3%)

Memory

0.3MiB live, 603.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 404×	`accelerator-lowering-fma.f32`
10 404×	`accelerator-lowering-fma.f64`
7 594×	`-lowering-.f32`
7 594×	`-lowering-.f64`
3 838×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	340	5206
1	1121	4921
2	3802	4921
0	8102	4483

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 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)))
(* 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))))))))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 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))))))))))
(* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))
(* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))
(* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))
(* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))
(* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* 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)) (* -1/16 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(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))))
(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))))

Outputs
x
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal -1/24 binary64) (.f64 eps (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal -1/24 binary64) (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 #s(literal 2 binary64) (.f64 eps (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 eps (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))))) (.f64 #s(literal -2 binary64) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (*.f64 x eps))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 eps (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))))) (.f64 x (-.f64 (.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (*.f64 eps #s(literal -1/48 binary64))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 eps (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))))) (.f64 x (+.f64 (.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 x (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 x eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 eps (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(* 1/2 (* eps (cos x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
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(* 1/24 (* eps (pow x 4)))
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(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(* eps (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))
(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(* 1/24 (* eps (pow x 2)))
(.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(* -1/720 (* eps (pow x 4)))
(.f64 (.f64 x x) (.f64 eps (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* -1/720 (* eps (pow x 4)))
(.f64 (.f64 x x) (.f64 eps (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/720 binary64)) (/.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x x))))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(* eps (pow x 2))
(.f64 x (.f64 x eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/8 binary64)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))

eval136.0ms (0.9%)

Memory: 32.3MiB live, 301.2MiB allocated
Compiler: Compiled 36 715 to 2 543 computations (93.1% saved)

prune91.0ms (0.6%)

Memory

-12.7MiB live, 187.8MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1 113	6	1 119
Fresh	4	0	4
Picked	3	2	5
Done	0	0	0
Total	1 120	8	1 128

Accuracy

100.0%

Counts

1 128 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)
✓	99.7%	(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
▶	99.5%	(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
	54.7%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	26.2%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))))))
▶	100.0%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
▶	99.9%	(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
✓	98.5%	eps

Compiler

Compiled 310 to 168 computations (45.8% saved)

simplify415.0ms (2.8%)

Memory

-16.6MiB live, 629.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
✓	cost-diff	0	(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
✓	cost-diff	0	(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
✓	cost-diff	0	(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (*.f64 x x))
✓	cost-diff	128	(+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x)))))
✓	cost-diff	768	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))
✓	cost-diff	0	(.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))
✓	cost-diff	0	(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	cost-diff	0	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
✓	cost-diff	0	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))

Rules

16 558×	`accelerator-lowering-fma.f32`
16 558×	`accelerator-lowering-fma.f64`
4 298×	`-lowering-.f32`
4 298×	`-lowering-.f64`
2 316×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	347
1	115	335
2	383	319
3	1263	317
4	3062	311
5	4093	311
6	5230	311
7	7038	311
0	8050	282

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps))))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
1/2
(* -1/48 (* eps eps))
-1/48
(* eps eps)
(cos (+ x (* 1/2 eps)))
(+ x (* 1/2 eps))
x
(* 1/2 eps)
2
(+ eps (* (* x x) (* eps -1/2)))
eps
(* (* x x) (* eps -1/2))
(* x x)
x
(* eps -1/2)
-1/2
(+ (* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))) eps)
(* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
x
(* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
(* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))
eps
(+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))
-1/2
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(* x x)
(+ 1/24 (* x (* x -1/720)))
1/24
(* x (* x -1/720))
(* x -1/720)
-1/720
(* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))
(* (* x x) (* x x))
(* x x)
x
(+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x)))))
(* -1/2 (/ eps (* x x)))
-1/2
(/ eps (* x x))
eps
(+ (* eps 1/24) (/ eps (* (* x x) (* x x))))
(* eps 1/24)
1/24
(/ eps (* (* x x) (* x x)))
(* eps (cos (+ x (* 1/2 eps))))
eps
(cos (+ x (* 1/2 eps)))
(+ x (* 1/2 eps))
x
(* 1/2 eps)
1/2

Outputs
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps #s(literal 2 binary64))))
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps))))
(.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
(+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))
1/2
#s(literal 1/2 binary64)
(* -1/48 (* eps eps))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
-1/48
#s(literal -1/48 binary64)
(* eps eps)
(*.f64 eps eps)
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ eps (* (* x x) (* eps -1/2)))
(.f64 eps (+.f64 (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))
eps
(* (* x x) (* eps -1/2))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* x x)
(*.f64 x x)
x
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(+ (* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))) eps)
(.f64 eps (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) #s(literal 1 binary64)))
(* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))) (.f64 eps (*.f64 x x)))
x
(* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))) (.f64 eps x))
(* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
eps
(+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
-1/2
#s(literal -1/2 binary64)
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/24 (* x (* x -1/720)))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
1/24
#s(literal 1/24 binary64)
(* x (* x -1/720))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* x -1/720)
(*.f64 x #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)
(* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))
(.f64 eps (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
x
(+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x)))))
(+.f64 (/.f64 eps (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* -1/2 (/ eps (* x x)))
(/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
-1/2
#s(literal -1/2 binary64)
(/ eps (* x x))
(/.f64 eps (*.f64 x x))
eps
(+ (* eps 1/24) (/ eps (* (* x x) (* x x))))
(+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 eps (.f64 x (.f64 x (.f64 x x)))))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(/ eps (* (* x x) (* x x)))
(/.f64 eps (.f64 x (.f64 x (*.f64 x x))))
(* eps (cos (+ x (* 1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
eps
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize143.0ms (1%)

Memory

22.9MiB live, 306.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) eps)
✓	accuracy	100.0%	(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
✓	accuracy	100.0%	(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/24 binary64))
✓	accuracy	92.6%	(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
✓	accuracy	59.1%	(/.f64 eps (*.f64 x x))
✓	accuracy	27.2%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))))))
✓	accuracy	99.9%	(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
✓	accuracy	99.7%	(.f64 x (.f64 x #s(literal -1/720 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
✓	accuracy	99.6%	(*.f64 x #s(literal -1/720 binary64))
✓	accuracy	100.0%	(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	99.9%	(.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	accuracy	100.0%	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
✓	accuracy	99.6%	(.f64 #s(literal -1/48 binary64) (.f64 eps eps))

Samples

80.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 349 to 41 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 34.0ms (58.4% of total)

const: 9.0ms (15.5% of total)

ival-add: 9.0ms (15.5% of total)

ival-div: 3.0ms (5.2% of total)

ival-cos: 2.0ms (3.4% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series32.0ms (0.2%)

Memory

6.7MiB live, 83.3MiB allocated

Counts

26 → 492

Calls

Call 1

Inputs
#<alt (* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)>
#<alt (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps))))>
#<alt (* eps (+ 1/2 (* -1/48 (* eps eps))))>
#<alt (+ 1/2 (* -1/48 (* eps eps)))>
#<alt (+ eps (* (* x x) (* eps -1/2)))>
#<alt (* (* x x) (* eps -1/2))>
#<alt (* x x)>
#<alt (* eps -1/2)>
#<alt (+ (* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))) eps)>
#<alt (* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))>
#<alt (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))>
#<alt (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))>
#<alt (* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))>
#<alt (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x)))))>
#<alt (* (* x x) (* x x))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* -1/48 (* eps eps))>
#<alt (* x -1/720)>
#<alt (* (* x x) (+ 1/24 (* x (* x -1/720))))>
#<alt (* x (* x -1/720))>
#<alt (/ eps (* x x))>
#<alt (/ eps (* (* x x) (* x x)))>
#<alt (* eps 1/24)>

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

Calls

123 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)
2.0ms	eps	@	0	(* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))
2.0ms	x	@	0	(* eps (cos (+ x (* 1/2 eps))))
2.0ms	eps	@	inf	(* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))
1.0ms	x	@	inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)

rewrite439.0ms (3%)

Memory

18.7MiB live, 764.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 310×	`-lowering-.f32`
5 310×	`-lowering-.f64`
4 120×	`/-lowering-/.f32`
4 120×	`/-lowering-/.f64`
3 468×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	254
1	237	244
2	2098	240
0	8451	218

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 708

Calls

Call 1

Inputs
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps)))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (+ x (* 1/2 eps))))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(+ 1/2 (* -1/48 (* eps eps)))
(+ eps (* (* x x) (* eps -1/2)))
(* (* x x) (* eps -1/2))
(* x x)
(* eps -1/2)
(+ (* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))) eps)
(* x (* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
(* x (* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
(* eps (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))
(* (* (* x x) (* x x)) (+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x))))))
(+ (* -1/2 (/ eps (* x x))) (+ (* eps 1/24) (/ eps (* (* x x) (* x x)))))
(* (* x x) (* x x))
(* eps (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* -1/48 (* eps eps))
(* x -1/720)
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(* x (* x -1/720))
(/ eps (* x x))
(/ eps (* (* x x) (* x x)))
(* eps 1/24)

Outputs
(.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
(.f64 eps (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
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(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 eps (*.f64 x x)))
(.f64 (/.f64 eps x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (.f64 x (*.f64 x x)) eps) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 eps x))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)

simplify707.0ms (4.8%)

Memory

-199.3MiB live, 808.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 706×	`accelerator-lowering-fma.f32`
12 706×	`accelerator-lowering-fma.f64`
7 408×	`-lowering-.f32`
7 408×	`-lowering-.f64`
4 752×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	338	5532
1	1105	5519
2	3686	5189
0	8175	4829

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* -1/24 (* (pow eps 3) (cos (+ x (* 1/2 eps)))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(* -1/24 (* (pow eps 3) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 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))))))))))
(* -1/48 (* (pow eps 3) (cos (+ x (* 1/2 eps)))))
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(* -1/48 (* (pow eps 3) (cos (- x (* -1/2 eps)))))
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1/2
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eps
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eps
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(* 1/24 eps)
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(* 1/24 eps)
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(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(/ eps (pow x 4))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* -1/24 (* (pow eps 3) (cos (+ x (* 1/2 eps)))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal -1/24 binary64) (.f64 eps (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* -1/24 (* (pow eps 3) (cos (- x (* -1/2 eps)))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal -1/24 binary64) (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (.f64 eps #s(literal -2 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+.f64 (.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (-.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps x))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (.f64 eps #s(literal -2 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (-.f64 (.f64 (.f64 eps #s(literal 1/3 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (*.f64 x x)))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos x)))
(.f64 (cos.f64 x) (.f64 eps #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)))))))))
(* -1/48 (* (pow eps 3) (cos (+ x (* 1/2 eps)))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* -1/48 (* (pow eps 3) (cos (- x (* -1/2 eps)))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps)))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/48 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 eps eps))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))
(.f64 eps (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+.f64 (.f64 eps (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 eps (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(+.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 eps (+.f64 (.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)))))) (.f64 x x)))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))
(.f64 eps (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))
(.f64 eps (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))
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(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))
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(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
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(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
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(* -1/2 eps)
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(* -1/720 (* eps (pow x 4)))
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(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
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(* -1/720 (* eps (pow x 4)))
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(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
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eps
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(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))))
(* 1/24 (* eps (pow x 4)))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
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(* 1/24 (* eps (pow x 4)))
(.f64 (.f64 eps (.f64 x x)) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
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(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
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(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(/ eps (pow x 4))
(/.f64 eps (.f64 (.f64 x x) (*.f64 x x)))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))

eval169.0ms (1.1%)

Memory: -0.5MiB live, 281.2MiB allocated
Compiler: Compiled 57 126 to 3 513 computations (93.9% saved)

prune122.0ms (0.8%)

Memory

9.8MiB live, 208.3MiB allocated

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	1 432	5	1 437
Fresh	0	1	1
Picked	1	4	5
Done	0	2	2
Total	1 433	12	1 445

Accuracy

100.0%

Counts

1 445 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)
✓	99.7%	(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
✓	99.5%	(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
	54.7%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	26.1%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) eps)) (/.f64 eps (.f64 x (.f64 x (.f64 x x))))) (*.f64 eps #s(literal 1/24 binary64))))
	25.5%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 (/.f64 (/.f64 eps (.f64 x x)) x) x))))
	25.5%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (+.f64 (.f64 eps #s(literal 1/24 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (/.f64 eps (*.f64 x x)))))))
	24.2%	(.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/24 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
✓	100.0%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	56.5%	(.f64 x (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (.f64 x x)))))
✓	99.9%	(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
✓	98.5%	eps

Compiler

Compiled 735 to 287 computations (61% saved)

regimes26.0ms (0.2%)

Memory

-6.7MiB live, 32.6MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))

Calls

3 calls:

9.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

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)

regimes12.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Counts

18 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	eps
5.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

-24.2MiB live, 14.6MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)

Calls

2 calls:

5.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (.f64 x x)))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (.f64 x x)))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
eps

Outputs
eps

Calls

2 calls:

1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

-27.4MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Rules

50×	`*-commutative_binary64`
24×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	102
1	89	102

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps

Outputs
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 eps (cos.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) eps)
(+.f64 eps (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(+.f64 eps (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps

soundness982.0ms (6.7%)

Memory

23.5MiB live, 650.8MiB allocated

Rules

16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
11 624×	`accelerator-lowering-fma.f32`
11 624×	`accelerator-lowering-fma.f64`
10 404×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	225
1	199	219
2	1678	219
0	8371	198
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	381	3514
1	1150	3346
2	3225	3310
0	8202	3062
0	340	5206
1	1121	4921
2	3802	4921
0	8102	4483
0	6	16
1	49	16
2	376	16
3	4763	16
0	8212	16

Stop Event

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

Compiler

Compiled 296 to 179 computations (39.5% saved)

preprocess126.0ms (0.9%)

Memory: -1.6MiB live, 194.5MiB allocated
Compiler: Compiled 320 to 176 computations (45% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

analyze77.0ms (0.5%)

sample6.5s (44.3%)

preprocess27.0ms (0.2%)

explain88.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize46.0ms (0.3%)

series4.0ms (0%)

rewrite328.0ms (2.2%)

simplify440.0ms (3%)

eval52.0ms (0.3%)

prune34.0ms (0.2%)

simplify453.0ms (3.1%)

localize212.0ms (1.4%)

series29.0ms (0.2%)

rewrite452.0ms (3.1%)

simplify428.0ms (2.9%)

eval134.0ms (0.9%)

prune99.0ms (0.7%)

simplify420.0ms (2.8%)

localize151.0ms (1%)

series43.0ms (0.3%)

rewrite606.0ms (4.1%)

simplify637.0ms (4.3%)

eval136.0ms (0.9%)

prune91.0ms (0.6%)

simplify415.0ms (2.8%)

localize143.0ms (1%)

series32.0ms (0.2%)

rewrite439.0ms (3%)

simplify707.0ms (4.8%)

eval169.0ms (1.1%)

prune122.0ms (0.8%)

regimes26.0ms (0.2%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

simplify9.0ms (0.1%)

soundness982.0ms (6.7%)

preprocess126.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18