Metrics for 2sin (example 3.3)

analyze41.0ms (0.3%)

Memory

0.2MiB live, 83.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.3s (39.8%)

Memory

156.1MiB live, 8 557.6MiB allocated

Samples

3.3s	25 729×	0	invalid
695.0ms	5 474×	0	valid
433.0ms	2 782×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.2s

ival-sin: 652.0ms (20.6% of total)

const: 646.0ms (20.4% of total)

ival-add: 528.0ms (16.7% of total)

ival-mult: 269.0ms (8.5% of total)

ival-<=: 256.0ms (8.1% of total)

ival-sub: 220.0ms (6.9% of total)

ival-fabs: 214.0ms (6.8% of total)

ival-<: 171.0ms (5.4% of total)

ival-and: 104.0ms (3.3% of total)

adjust: 50.0ms (1.6% of total)

exact: 44.0ms (1.4% of total)

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

Bogosity

preprocess106.0ms (0.7%)

Memory

-17.5MiB live, 58.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

explain138.0ms (0.9%)

Memory

-5.5MiB live, 205.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
227	2	(-1.456526649577993e-179 1.426521064178421e-181)	4	(6.92236393186967e-49 1.145537085783642e-50)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	225	5
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	224	3
-	2	27

Precision

0.9911504424778761

Recall

0.986784140969163

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	224	3	0
-	2	1	26

Precision?

0.9869565217391304

Recall?

1.0

Freqs

test

number	freq
0	30
1	225
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms	166×	1	valid
17.0ms	346×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sin: 9.0ms (36.6% of total)

ival-sub: 9.0ms (36.6% of total)

adjust: 3.0ms (12.2% of total)

ival-add: 3.0ms (12.2% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize34.0ms (0.2%)

Memory

-23.4MiB live, 54.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

16.0ms	173×	0	valid
10.0ms	83×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-add: 12.0ms (61.5% of total)

ival-sin: 5.0ms (25.6% of total)

adjust: 1.0ms (5.1% of total)

ival-sub: 1.0ms (5.1% of total)

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

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

series4.0ms (0%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite366.0ms (2.3%)

Memory

-7.2MiB live, 604.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

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

simplify568.0ms (3.6%)

Memory

6.0MiB live, 670.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

eval39.0ms (0.2%)

Memory: 8.9MiB live, 88.6MiB allocated
Compiler: Compiled 7 746 to 844 computations (89.1% saved)

prune36.0ms (0.2%)

Memory

17.3MiB live, 130.0MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	285	6	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	285	7	292

Accuracy

100.0%

Counts

292 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.9%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
▶	99.7%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
▶	99.0%	(*.f64 eps (cos.f64 x))
▶	97.5%	(sin.f64 eps)

Compiler

Compiled 167 to 112 computations (32.9% saved)

simplify512.0ms (3.2%)

Memory

-10.9MiB live, 482.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

10 248×	`lower-fma.f32`
10 242×	`lower-fma.f64`
7 504×	`lower-*.f32`
7 486×	`lower-*.f64`
5 192×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	145
0	52	129
1	87	129
2	189	129
3	372	125
4	580	125
5	1221	125
6	2406	125
7	3079	125
8	3537	125
9	3761	125
10	3992	125
11	4153	125
12	4954	125
13	5274	125
14	5371	125
15	5408	125
16	5434	125
17	5450	125
18	5458	125
19	5458	125
20	5458	125
21	5580	125
22	5632	125
23	5632	125
24	5632	125
0	9098	121

Stop Event

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

Calls

Call 1

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

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

localize126.0ms (0.8%)

Memory

3.9MiB live, 196.8MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
✓	accuracy	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	62.7%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

52.0ms	82×	1	valid
36.0ms	174×	0	valid

Compiler

Compiled 156 to 33 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-add: 25.0ms (37.7% of total)

ival-mult: 18.0ms (27.1% of total)

ival-sin: 9.0ms (13.6% of total)

adjust: 4.0ms (6% of total)

ival-cos: 4.0ms (6% of total)

const: 4.0ms (6% of total)

ival-sub: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series27.0ms (0.2%)

Memory

18.5MiB live, 55.1MiB allocated

Counts

18 → 336

Calls

Call 1

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

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<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 (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (- (sin x) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<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 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

84 calls:

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

rewrite482.0ms (3%)

Memory

-45.2MiB live, 401.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 910×	`lower-fma.f32`
5 904×	`lower-fma.f64`
4 274×	`lower-/.f64`
4 274×	`lower-/.f32`
4 206×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	117
0	52	103
1	162	103
2	1363	103
0	8194	103

Stop Event

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

Counts

18 → 714

Calls

Call 1

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

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

simplify911.0ms (5.7%)

Memory

9.1MiB live, 359.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 362×	`lower-fma.f64`
12 362×	`lower-fma.f32`
5 480×	`lower-*.f64`
5 480×	`lower-*.f32`
4 416×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	2877
1	1144	2755
2	3078	2719
3	7787	2719
0	8296	2496

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 310

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
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)))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(- (sin x) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (cos x))) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(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 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
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)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (neg.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal -2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 1/2 (* eps (cos x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.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))))))))))
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(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/10080 binary64)) #s(literal -1/240 binary64))) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)) (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval332.0ms (2.1%)

Memory: 24.1MiB live, 159.4MiB allocated
Compiler: Compiled 28 192 to 2 556 computations (90.9% saved)

prune205.0ms (1.3%)

Memory

-14.9MiB live, 261.1MiB allocated

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	1 019	18	1 037
Fresh	1	0	1
Picked	3	2	5
Done	1	0	1
Total	1 024	20	1 044

Accuracy

100.0%

Counts

1 044 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
	98.4%	(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
	99.7%	(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
	98.4%	(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
	99.5%	(/.f64 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	99.9%	(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))
	98.6%	(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
	98.4%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
▶	98.4%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	98.3%	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
	99.1%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
	99.1%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	99.7%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	99.0%	(*.f64 eps (cos.f64 x))
▶	97.5%	(*.f64 eps #s(literal 1 binary64))
	5.8%	(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))

Compiler

Compiled 618 to 386 computations (37.5% saved)

simplify409.0ms (2.6%)

Memory

8.3MiB live, 607.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
✓	cost-diff	320	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	cost-diff	320	(*.f64 eps #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

15 886×	`lower-fma.f32`
15 872×	`lower-fma.f64`
5 108×	`lower-*.f32`
5 072×	`lower-*.f64`
3 052×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	341
0	84	315
1	174	281
2	575	279
3	2236	279
4	3014	279
5	3403	279
6	3902	279
7	5679	279
8	7232	279
0	8054	273

Stop Event

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

Calls

Call 1

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

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

localize169.0ms (1.1%)

Memory

4.9MiB live, 359.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(*.f64 eps #s(literal -1/48 binary64))
✓	accuracy	100.0%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
✓	accuracy	100.0%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
✓	accuracy	99.5%	(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
✓	accuracy	100.0%	(fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1 binary64))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Samples

102.0ms	253×	0	valid
4.0ms	2×	5	exit
1.0ms	1×	3	valid

Compiler

Compiled 365 to 52 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 35.0ms (49.4% of total)

const: 11.0ms (15.5% of total)

ival-add: 10.0ms (14.1% of total)

ival-cos: 5.0ms (7.1% of total)

ival-sin: 5.0ms (7.1% of total)

adjust: 2.0ms (2.8% of total)

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

exact: 1.0ms (1.4% of total)

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

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

series42.0ms (0.3%)

Memory

2.6MiB live, 89.8MiB allocated

Counts

23 → 432

Calls

Call 1

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

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<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 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) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 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 (- (* (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 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (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) (* (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 (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))>
#<alt (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))>
#<alt (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))>
#<alt (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))>
#<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 (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* eps (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* 1/24 eps)>
#<alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))>
#<alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))>
#<alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))>
#<alt (* -1/720 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* -1/720 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 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 x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -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))))))))>
#<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 (* 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 (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 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 (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -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))))))))>
#<alt (* -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))))))))>
#<alt (* -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))))))))>
#<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 (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 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 (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))>
#<alt (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* x (sin (* 1/2 eps)))>
#<alt (* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))>
#<alt (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))>
#<alt (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt 1/24>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

108 calls:

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

rewrite362.0ms (2.3%)

Memory

-6.2MiB live, 498.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 504×	`lower-*.f32`
4 468×	`lower-*.f64`
4 116×	`lower-fma.f32`
4 102×	`lower-fma.f64`
3 924×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	266
0	84	252
1	292	191
2	2573	191
0	8258	184

Stop Event

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

Counts

23 → 1 015

Calls

Call 1

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

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

simplify411.0ms (2.6%)

Memory

2.0MiB live, 475.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 244×	`lower-fma.f64`
13 244×	`lower-fma.f32`
6 822×	`lower-*.f64`
6 822×	`lower-*.f32`
3 600×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	405	5527
1	1339	5335
2	4474	5182
0	8086	4838

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 391

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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))))
(* 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
(+ 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
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* 1/24 (pow x 3))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (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 (- (* (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))))))))
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))))))
(* 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)))
(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 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 eps)
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(* -1/720 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* -1/720 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 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)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* -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))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(cos x)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))

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

eval209.0ms (1.3%)

Memory: 37.3MiB live, 348.5MiB allocated
Compiler: Compiled 55 972 to 4 131 computations (92.6% saved)

prune170.0ms (1.1%)

Memory

-26.5MiB live, 367.4MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	1 480	11	1 491
Fresh	4	9	13
Picked	4	1	5
Done	0	2	2
Total	1 488	23	1 511

Accuracy

100.0%

Counts

1 511 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
	98.6%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
	98.4%	(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
	98.6%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
	99.7%	(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
▶	98.4%	(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
	98.3%	(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
	99.5%	(/.f64 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps))
	98.6%	(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
▶	98.4%	(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
	99.9%	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
	53.7%	(.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) eps) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.7%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
	98.4%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	98.4%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	99.1%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
	99.1%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	99.7%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	99.0%	(*.f64 eps (cos.f64 x))
	5.8%	(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
▶	97.5%	eps

Compiler

Compiled 733 to 444 computations (39.4% saved)

simplify334.0ms (2.1%)

Memory

7.1MiB live, 298.0MiB 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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	640	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 eps x)
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
✓	cost-diff	0	(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
✓	cost-diff	448	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))
✓	cost-diff	0	(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
✓	cost-diff	128	(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
✓	cost-diff	128	(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	14912	(.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))

Rules

5 248×	`lower-/.f32`
5 246×	`lower-/.f64`
5 184×	`lower-fma.f32`
5 174×	`lower-fma.f64`
4 546×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	313
0	80	331
1	147	321
2	391	249
3	1287	241
4	2570	241
5	3936	241
6	4856	241
7	5123	241
8	5141	241
9	5159	241
10	5549	241
11	5655	241
12	5907	241
13	6325	241
14	6384	241
15	6446	241
16	6499	241
17	6550	241
18	6610	241
19	6725	241
20	6927	241
0	9793	232

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
x
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
#s(literal 1 binary64)
#s(literal 2 binary64)
eps
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
(*.f64 x x)
x
(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
eps
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
x
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))
eps
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
#s(literal -1/2 binary64)
(+.f64 eps x)
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(*.f64 eps eps)
#s(literal 1/12 binary64)
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))
(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
(fma.f64 eps #s(literal -1/2 binary64) x)
x
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
#s(literal 1 binary64)
#s(literal 2 binary64)
eps
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps (*.f64 x x)) eps)
(.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps (.f64 x x)))
(*.f64 x x)
x
(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
eps
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 x (.f64 eps (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) eps)
x
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
eps
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
#s(literal -1/2 binary64)
(+.f64 eps x)
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(.f64 eps (.f64 #s(literal 1/12 binary64) (.f64 eps (.f64 x x))))
(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(.f64 eps (.f64 x (*.f64 eps #s(literal 1/12 binary64))))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(*.f64 eps eps)
#s(literal 1/12 binary64)
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)

localize145.0ms (0.9%)

Memory

14.9MiB live, 214.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
✓	accuracy	99.8%	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
✓	accuracy	100.0%	(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
✓	accuracy	99.9%	(.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
✓	accuracy	100.0%	(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

88.0ms

256×

valid

Compiler

Compiled 333 to 49 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 35.0ms (56% of total)

ival-add: 11.0ms (17.6% of total)

const: 6.0ms (9.6% of total)

ival-cos: 5.0ms (8% of total)

ival-div: 2.0ms (3.2% of total)

ival-sin: 2.0ms (3.2% of total)

exact: 1.0ms (1.6% of total)

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

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

series39.0ms (0.2%)

Memory

-4.3MiB live, 32.6MiB allocated

Counts

24 → 516

Calls

Call 1

Inputs
#<alt (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))>
#<alt (+.f64 eps #s(literal 0 binary64))>
#<alt (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))>
#<alt (+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)>
#<alt (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))>
#<alt (*.f64 x x)>
#<alt (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)>
#<alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))>
#<alt (fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)>
#<alt (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))>
#<alt (+.f64 eps x)>
#<alt (.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))>
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))>
#<alt (*.f64 eps #s(literal 1/2 binary64))>
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))>
#<alt (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (*.f64 x #s(literal 1/24 binary64))>
#<alt (.f64 (.f64 eps eps) #s(literal 1/12 binary64))>
#<alt (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))>
#<alt (.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))>
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))>

Outputs
#<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 eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt 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 (- (/ x eps) 1/2))>
#<alt (* eps (- (/ x eps) 1/2))>
#<alt (* eps (- (/ x eps) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 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) (* 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 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (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) (* 1/24 (* eps (pow x 2)))))>
#<alt (* (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)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<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)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* eps (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<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) (* 1/24 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))>
#<alt (* 1/24 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* 1/24 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
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#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
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#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
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#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* -1/2 x)>
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#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<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 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 (* 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 (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<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)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<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 (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))))))>
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#<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 (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)))>
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#<alt (cos (+ x (* 1/2 eps)))>
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#<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 (* -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)))>
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#<alt (cos (+ x (* -1/2 eps)))>
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#<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)))))>
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#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
#<alt (cos (- x (* 1/2 eps)))>
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#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (cos (+ x (* -1/2 eps)))>
#<alt (* (cos (* -1/2 eps)) (cos (* 1/2 eps)))>
#<alt (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1 (* (cos (* 1/2 eps)) (sin (* -1/2 eps)))))) (* (cos (* -1/2 eps)) (cos (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (+ (* -1 (* (cos (* 1/2 eps)) (sin (* -1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 eps)))) (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))) (* (cos (* -1/2 eps)) (cos (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (+ (* -1 (* (cos (* 1/2 eps)) (sin (* -1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 eps)))) (+ (* x (+ (* 1/6 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (+ (* 1/6 (* (cos (* 1/2 eps)) (sin (* -1/2 eps)))) (+ (* 1/2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* 1/2 (* (cos (* 1/2 eps)) (sin (* -1/2 eps)))))))) (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))) (* (cos (* -1/2 eps)) (cos (* 1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (+ x (* 1/2 eps))))>
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#<alt (* (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* (cos (- (* -1/2 eps) (* -1 x))) (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (pow (cos x) 2)>
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#<alt (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/4 (pow (cos x) 2)) (* -1/4 (pow (sin x) 2))))))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/4 (pow (cos x) 2)) (+ (* -1/4 (pow (sin x) 2)) (* eps (+ (* -1/16 (* (cos x) (sin x))) (+ (* -1/48 (* (cos x) (sin x))) (+ (* 1/48 (* (cos x) (sin x))) (* 1/16 (* (cos x) (sin x))))))))))))) (pow (cos x) 2))>
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#<alt (* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

129 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (* (* (cos (+ x (* eps -1/2))) (cos (+ (* 1/2 eps) x))) (/ 1 (cos (+ x (* eps -1/2)))))) 2)
1.0ms	x	@	0	(* (cos (+ x (* eps -1/2))) (cos (+ (* 1/2 eps) x)))
1.0ms	eps	@	inf	(+ (* eps (* -1/2 (+ eps x))) (* x (* x (* (* eps eps) 1/12))))
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (* (* (cos (+ x (* eps -1/2))) (cos (+ (* 1/2 eps) x))) (/ 1 (cos (+ x (* eps -1/2)))))) 2)
1.0ms	eps	@	0	(+ (* eps (* -1/2 (+ eps x))) (* x (* x (* (* eps eps) 1/12))))

rewrite439.0ms (2.8%)

Memory

-1.9MiB live, 278.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 634×	`lower-*.f32`
4 598×	`lower-*.f64`
4 126×	`lower-/.f32`
4 124×	`lower-/.f64`
3 682×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	226
0	80	218
1	275	218
2	2169	188
0	8240	184

Stop Event

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

Counts

24 → 678

Calls

Call 1

Inputs
(.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(+.f64 eps #s(literal 0 binary64))
(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps))
(*.f64 x x)
(.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(+.f64 eps x)
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(*.f64 eps #s(literal 1/2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 x #s(literal 1/24 binary64))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Outputs
(/.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))))
(/.f64 (.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(/.f64 (.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal -1 binary64) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))) (.f64 (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))) (neg.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 1 binary64))) (neg.f64 (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -1 binary64))) (neg.f64 (.f64 #s(literal 2 binary64) (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))))) (neg.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))))) (neg.f64 (.f64 (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (neg.f64 (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (*.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) (neg.f64 (neg.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(pow.f64 (/.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -1 binary64))
(*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))
(*.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
eps
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) 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 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps (.f64 eps eps))) eps) (.f64 (neg.f64 (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (neg.f64 (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(/.f64 (neg.f64 (neg.f64 (.f64 eps (.f64 eps eps)))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(+.f64 x (*.f64 eps #s(literal -1/2 binary64)))
(+.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(fma.f64 eps #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) eps x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64))) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x x)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64))) (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (*.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x))) (neg.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x (.f64 eps #s(literal -1/2 binary64)))))))
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(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -1 binary64))
(*.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (+.f64 (cos.f64 (+.f64 x (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) (cos.f64 (-.f64 (fma.f64 eps #s(literal -1/2 binary64) x) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/12 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal 1/12 binary64))) eps)
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/12 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal 1/12 binary64)))) (neg.f64 eps))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/12 binary64)) eps)
(.f64 x (.f64 eps (*.f64 eps #s(literal 1/12 binary64))))
(.f64 eps (.f64 (*.f64 eps #s(literal 1/12 binary64)) x))
(.f64 (.f64 eps eps) (*.f64 #s(literal 1/12 binary64) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(.f64 (.f64 eps (*.f64 eps #s(literal 1/12 binary64))) x)
(.f64 (.f64 x eps) (*.f64 eps #s(literal 1/12 binary64)))
(.f64 (.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64))
(.f64 (.f64 x #s(literal 1/12 binary64)) (*.f64 eps eps))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))
(.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x x))
(.f64 (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))) x)
(.f64 (.f64 x (.f64 eps eps)) (.f64 #s(literal 1/12 binary64) x))
(.f64 (.f64 (.f64 x x) eps) (.f64 eps #s(literal 1/12 binary64)))
(.f64 (.f64 x (.f64 x (.f64 eps eps))) #s(literal 1/12 binary64))
(.f64 (.f64 (.f64 x x) (.f64 eps eps)) #s(literal 1/12 binary64))
(.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 eps eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))

simplify544.0ms (3.4%)

Memory

26.9MiB live, 412.3MiB allocated

Algorithm

1×	egg-herbie

Rules

15 054×	`lower-fma.f64`
15 054×	`lower-fma.f32`
7 468×	`lower-*.f64`
7 468×	`lower-*.f32`
2 706×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	465	5302
1	1463	5045
2	4331	5038
0	8441	4592

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 490

Calls

Call 1

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

Outputs
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 x (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal 1/6 binary64)))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/8 binary64)))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
x
(* x (+ 1 (* -1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* x (+ 1 (* -1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* x (+ 1 (* -1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
x
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* -1 (* x (- (* 1/2 (/ eps x)) 1)))
(fma.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
x
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
(+ x (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) x)
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* eps (- (/ x eps) 1/2))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(* eps (- (/ x eps) 1/2))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(* eps (- (/ 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 (* eps (+ 1/2 (* -1 (/ x eps)))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (+ 1/2 (* -1 (/ x eps)))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
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(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (pow (cos x) 2))
(+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/4 (pow (cos x) 2)) (* -1/4 (pow (sin x) 2))))))) (pow (cos x) 2))
(fma.f64 eps (*.f64 eps #s(literal -1/4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/4 (pow (cos x) 2)) (+ (* -1/4 (pow (sin x) 2)) (* eps (+ (* -1/16 (* (cos x) (sin x))) (+ (* -1/48 (* (cos x) (sin x))) (+ (* 1/48 (* (cos x) (sin x))) (* 1/16 (* (cos x) (sin x))))))))))))) (pow (cos x) 2))
(fma.f64 eps (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 (sin.f64 x) #s(literal 1/12 binary64)) (.f64 (sin.f64 x) (.f64 (cos.f64 x) #s(literal -1/12 binary64)))) #s(literal -1/4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* 1/2 eps))) (cos (- x (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* (cos (+ x (* -1/2 eps))) (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 x (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal 1/6 binary64)))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/8 binary64)))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

eval208.0ms (1.3%)

Memory: -17.0MiB live, 262.9MiB allocated
Compiler: Compiled 45 648 to 3 392 computations (92.6% saved)

prune230.0ms (1.4%)

Memory

-8.5MiB live, 233.6MiB allocated

Pruning

26 alts after pruning (21 fresh and 5 done)

	Pruned	Kept	Total
New	1 260	9	1 269
Fresh	3	12	15
Picked	3	2	5
Done	0	3	3
Total	1 266	26	1 292

Accuracy

100.0%

Counts

1 292 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
	98.6%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
	98.4%	(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
	98.6%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
	99.7%	(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
	98.3%	(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
	98.3%	(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
	97.5%	(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
	98.4%	(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
	97.5%	(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
	98.6%	(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
✓	98.4%	(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
	98.3%	(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
	99.9%	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
	53.7%	(.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) eps) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64)))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	36.7%	(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
	5.5%	(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
✓	98.4%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	99.1%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
✓	99.7%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
	99.7%	(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	99.0%	(*.f64 eps (cos.f64 x))
	5.8%	(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
✓	97.5%	eps

Compiler

Compiled 1 102 to 445 computations (59.6% saved)

regimes37.0ms (0.2%)

Memory

12.4MiB live, 51.0MiB allocated

Counts

45 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) eps) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))
(/.f64 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x
11.0ms	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)

regimes37.0ms (0.2%)

Memory

6.9MiB live, 83.9MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) eps) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))
(/.f64 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

12.0ms	eps
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

-26.3MiB live, 53.3MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

31.0MiB live, 68.7MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (cos.f64 x)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-29.6MiB live, 49.2MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))

Outputs
(*.f64 eps (cos.f64 x))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Memory

38.3MiB live, 38.3MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))
(+.f64 (+.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 x x))))
(.f64 x (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (.f64 x x))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 eps (.f64 x (.f64 x x)))))))
(sin.f64 eps)

Outputs

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

Calls

3 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

-27.7MiB live, 35.3MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) x) x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))

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

Calls

3 calls:

17.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-5.3MiB live, 34.3MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)

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

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-9.0MiB live, 30.5MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-14.3MiB live, 24.9MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps)
(+.f64 (.f64 (.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps x)) eps)
(.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 eps eps)))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 eps eps)))) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps)
(+.f64 (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 eps (fma.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) eps)
(fma.f64 x (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps)

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

-29.5MiB live, 11.2MiB allocated

Accuracy

Total -58.7b remaining (-3640.1%)

Threshold costs -58.7b (-3640.1%)

Counts

3 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))

Outputs
eps

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`eps`
97.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

29.2MiB live, 29.2MiB allocated

Algorithm

1×	egg-herbie

Rules

70×	`*-commutative_binary64`
16×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	198
1	121	198
2	132	198
3	138	198
4	142	198
5	143	198

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (9.5%)

Memory

6.0MiB live, 1 388.6MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
15 054×	`lower-fma.f64`
15 054×	`lower-fma.f32`
13 244×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	266
0	84	252
1	292	191
2	2573	191
0	8258	184
0	465	5302
1	1463	5045
2	4331	5038
0	8441	4592
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	375	2877
1	1144	2755
2	3078	2719
3	7787	2719
0	8296	2496
0	28	117
0	52	103
1	162	103
2	1363	103
0	8194	103
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	405	5527
1	1339	5335
2	4474	5182
0	8086	4838

Stop Event

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

Compiler

Compiled 496 to 260 computations (47.6% saved)

preprocess126.0ms (0.8%)

Memory: -18.8MiB live, 295.7MiB allocated
Compiler: Compiled 512 to 222 computations (56.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

analyze41.0ms (0.3%)

sample6.3s (39.8%)

preprocess106.0ms (0.7%)

explain138.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize34.0ms (0.2%)

series4.0ms (0%)

rewrite366.0ms (2.3%)

simplify568.0ms (3.6%)

eval39.0ms (0.2%)

prune36.0ms (0.2%)

simplify512.0ms (3.2%)

localize126.0ms (0.8%)

series27.0ms (0.2%)

rewrite482.0ms (3%)

simplify911.0ms (5.7%)

eval332.0ms (2.1%)

prune205.0ms (1.3%)

simplify409.0ms (2.6%)

localize169.0ms (1.1%)

series42.0ms (0.3%)

rewrite362.0ms (2.3%)

simplify411.0ms (2.6%)

eval209.0ms (1.3%)

prune170.0ms (1.1%)

simplify334.0ms (2.1%)

localize145.0ms (0.9%)

series39.0ms (0.2%)

rewrite439.0ms (2.8%)

simplify544.0ms (3.4%)

eval208.0ms (1.3%)

prune230.0ms (1.4%)

regimes37.0ms (0.2%)

regimes37.0ms (0.2%)

regimes31.0ms (0.2%)

regimes27.0ms (0.2%)

regimes22.0ms (0.1%)

regimes20.0ms (0.1%)

regimes29.0ms (0.2%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

regimes15.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0%)

regimes7.0ms (0%)

simplify10.0ms (0.1%)

soundness1.5s (9.5%)

preprocess126.0ms (0.8%)

end0.0ms (0%)

Profiling

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

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