Metrics for 2sin (example 3.3)

analyze41.0ms (0.3%)

Memory

-3.1MiB live, 73.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.5s (45.3%)

Memory

-300.6MiB live, 7 729.0MiB allocated

Samples

3.6s	26 475×	0	invalid
636.0ms	5 509×	0	valid
416.0ms	2 747×	1	valid

Precisions

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

const: 673.0ms (21.2% of total)

ival-sin: 611.0ms (19.2% of total)

ival-add: 449.0ms (14.1% of total)

ival-<=: 314.0ms (9.9% of total)

ival-fabs: 276.0ms (8.7% of total)

ival-mult: 262.0ms (8.2% of total)

ival-sub: 232.0ms (7.3% of total)

ival-<: 149.0ms (4.7% of total)

ival-and: 105.0ms (3.3% of total)

adjust: 49.0ms (1.5% of total)

exact: 46.0ms (1.4% of total)

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

Bogosity

preprocess25.0ms (0.2%)

Memory

24.0MiB live, 24.0MiB 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))

explain147.0ms (1%)

Memory

-21.5MiB live, 63.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
228	0	-	4	(-1.0990040264095181e-305 1.3442767363283712e-307)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	1	(209.63040685519428 2.64194212535061e-12)	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	224	6
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	224	4
-	0	28

Precision

1.0

Recall

0.9824561403508771

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	224	3	1
-	0	3	25

Precision?

0.9869565217391304

Recall?

0.9956140350877193

Freqs

test

number	freq
0	32
1	222
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms	196×	1	valid
15.0ms	312×	0	valid
1.0ms	4×	3	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sin: 10.0ms (49.5% of total)

adjust: 3.0ms (14.8% of total)

ival-add: 3.0ms (14.8% of total)

ival-sub: 3.0ms (14.8% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize80.0ms (0.6%)

Memory

-8.3MiB live, 29.3MiB 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	60.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

64.0ms	98×	1	valid
8.0ms	156×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

adjust: 56.0ms (85.9% of total)

ival-sin: 5.0ms (7.7% of total)

ival-add: 2.0ms (3.1% of total)

ival-sub: 2.0ms (3.1% of total)

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

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

series4.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite361.0ms (2.5%)

Memory

20.1MiB live, 453.1MiB 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))

simplify361.0ms (2.5%)

Memory

-24.9MiB live, 698.2MiB 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)

eval36.0ms (0.2%)

Memory: -1.8MiB live, 75.9MiB allocated
Compiler: Compiled 7 746 to 844 computations (89.1% saved)

prune31.0ms (0.2%)

Memory

31.4MiB live, 69.5MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	287	4	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	287	5	292

Accuracy

100.0%

Counts

292 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.8%	(-.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 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
▶	99.6%	(*.f64 eps (cos.f64 x))
▶	97.9%	(sin.f64 eps)

Compiler

Compiled 49 to 34 computations (30.6% saved)

simplify534.0ms (3.7%)

Memory

-26.5MiB live, 422.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	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))
✓	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	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(sin.f64 eps)

Rules

24 364×	`associate-r`
11 286×	`lower-*.f32`
11 272×	`lower-*.f64`
10 976×	`lower-fma.f32`
10 972×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	106
0	38	96
1	61	96
2	126	96
3	218	92
4	251	92
5	283	92
6	356	92
7	537	92
8	608	92
9	608	92
10	964	92
11	1140	92
12	1140	92
13	1140	92
14	2271	92
15	2507	92
16	2673	92
17	2673	92
18	2673	92
19	2673	92
20	2673	92
21	6603	92
22	7163	92
23	7739	92
24	7739	92
25	7739	92
26	7739	92
27	7739	92
0	19794	88

Stop Event

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

Calls

Call 1

Inputs
(sin.f64 eps)
eps
(*.f64 eps (cos.f64 x))
eps
(cos.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)
(.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)

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

localize63.0ms (0.4%)

Memory

-4.0MiB live, 72.9MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	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)))
✓	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%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)

Samples

39.0ms

256×

valid

Compiler

Compiled 115 to 25 computations (78.3% saved)

Precisions

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

ival-mult: 13.0ms (51.3% of total)

ival-sin: 5.0ms (19.7% of total)

ival-add: 3.0ms (11.8% of total)

ival-cos: 3.0ms (11.8% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

13 → 240

Calls

Call 1

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

Outputs
#<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 (* 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 (* 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 (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))>

Calls

60 calls:

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

rewrite343.0ms (2.4%)

Memory

-6.2MiB live, 387.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 442×	`lower-fma.f32`
11 438×	`lower-fma.f64`
5 140×	`lower-*.f32`
5 126×	`lower-*.f64`
3 582×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	84
0	38	76
1	102	76
2	806	76
0	8435	76

Stop Event

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

Counts

13 → 593

Calls

Call 1

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

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

simplify389.0ms (2.7%)

Memory

6.1MiB live, 391.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 260×	`lower-fma.f64`
16 260×	`lower-fma.f32`
6 018×	`lower-*.f64`
6 018×	`lower-*.f32`
3 172×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	291	2090
1	893	1980
2	2341	1938
3	4842	1930
0	8433	1761

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 221

Calls

Call 1

Inputs
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)
(* 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)
(* 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)))
(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))

Outputs
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 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)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 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) (* -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)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 eps eps) (.f64 x #s(literal -1/2 binary64)) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/12 binary64) (.f64 (.f64 eps (.f64 eps x)) x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) 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 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
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 x (.f64 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 (.f64 x x) (fma.f64 (*.f64 x 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 (.f64 x x) (fma.f64 (.f64 x 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 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
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eval101.0ms (0.7%)

Memory: 4.3MiB live, 161.1MiB allocated
Compiler: Compiled 18 737 to 2 085 computations (88.9% saved)

prune101.0ms (0.7%)

Memory

5.6MiB live, 208.3MiB allocated

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	814	13	827
Fresh	0	0	0
Picked	2	2	4
Done	1	0	1
Total	817	15	832

Accuracy

100.0%

Counts

832 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
▶	98.6%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
	98.6%	(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
	98.6%	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
	52.7%	(.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps))
	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))
	99.8%	(.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))
	36.2%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.8%	(.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)))
	98.5%	(.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)))
▶	99.4%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
▶	99.5%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
✓	99.6%	(*.f64 eps (cos.f64 x))
▶	97.9%	(*.f64 eps #s(literal 1 binary64))

Compiler

Compiled 402 to 248 computations (38.3% saved)

simplify51.0ms (0.4%)

Memory

-18.3MiB live, 59.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
✓	cost-diff	320	(*.f64 eps #s(literal 1 binary64))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) (sin.f64 x))
✓	cost-diff	320	(fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))

Rules

1 104×	`lower-fma.f32`
1 092×	`lower-fma.f64`
976×	`lower-*.f32`
954×	`lower-*.f64`
686×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	144
0	50	142
1	108	142
2	303	141
3	715	141
4	988	141
5	1163	141
6	1293	141
7	1367	141
8	1367	141
9	1530	141
10	1653	141
0	1653	140

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize96.0ms (0.7%)

Memory

37.8MiB live, 154.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
✓	accuracy	100.0%	(fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/12 binary64))
✓	accuracy	100.0%	(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (cos.f64 x))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
✓	accuracy	100.0%	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1 binary64))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	99.9%	(.f64 (.f64 eps eps) (sin.f64 x))

Samples

64.0ms

256×

valid

Compiler

Compiled 159 to 33 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 30.0ms (64.3% of total)

ival-add: 7.0ms (15% of total)

const: 6.0ms (12.9% of total)

ival-cos: 2.0ms (4.3% of total)

ival-sin: 2.0ms (4.3% of total)

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

exact: 0.0ms (0% of total)

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

series28.0ms (0.2%)

Memory

-0.8MiB live, 36.8MiB allocated

Counts

19 → 336

Calls

Call 1

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

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

Calls

84 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(* x (+ (* x (* x 1/12)) -1/2))
4.0ms	x	@	-inf	(+ (* (* (* eps eps) (sin x)) -1/2) (* eps (cos x)))
1.0ms	eps	@	0	(+ (* (* x x) (* eps (+ (* (* x x) 1/24) -1/2))) eps)
1.0ms	eps	@	0	(* eps (+ (* eps (* x (+ (* x (* x 1/12)) -1/2))) (cos x)))
1.0ms	x	@	inf	(+ (* (* (* eps eps) (sin x)) -1/2) (* eps (cos x)))

rewrite421.0ms (2.9%)

Memory

-35.2MiB live, 576.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

12 208×	`lower-fma.f32`
12 196×	`lower-fma.f64`
5 600×	`lower-*.f32`
5 578×	`lower-*.f64`
3 574×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	124
0	50	122
1	181	122
2	1341	122
0	8369	122

Stop Event

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

Counts

19 → 502

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
(+.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
(+.f64 (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))) (neg.f64 (/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))) (/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (sin.f64 x)))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (fma.f64 eps (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (sin.f64 x)))))))
(fma.f64 eps (cos.f64 x) (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 eps (.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(fma.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (sin.f64 x))) (*.f64 eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1 binary64) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))) (neg.f64 (/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (sin.f64 x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x))))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (sin.f64 x)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 eps (cos.f64 x) (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (cos.f64 x) (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (.f64 eps (sin.f64 x))) (.f64 eps (cos.f64 x)))))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (sin.f64 x))))) (fma.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal 2 binary64))))))
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(.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x)
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) (.f64 x (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/12 binary64)) (.f64 x #s(literal -1/2 binary64)))))))
(.f64 (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(.f64 (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal -1/2 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))))
(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/12 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2985984 binary64)) #s(literal -1/512 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2985984 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/13824 binary64)))) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2985984 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2985984 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/20736 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/20736 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64))) (.f64 (.f64 x x) #s(literal -1/24 binary64))))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))
(*.f64 eps (cos.f64 x))
(*.f64 (cos.f64 x) eps)
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 eps (cos.f64 x)))
(*.f64 x #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) x)

simplify361.0ms (2.5%)

Memory

-0.6MiB live, 483.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 208×	`lower-fma.f64`
14 208×	`lower-fma.f32`
5 300×	`lower-*.f64`
5 300×	`lower-*.f32`
2 510×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	236	2923
1	773	2873
2	2453	2799
3	5300	2747
0	8330	2563

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 318

Calls

Call 1

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

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

eval122.0ms (0.8%)

Memory: 34.8MiB live, 224.7MiB allocated
Compiler: Compiled 23 591 to 1 859 computations (92.1% saved)

prune142.0ms (1%)

Memory

-22.5MiB live, 185.4MiB allocated

Pruning

20 alts after pruning (14 fresh and 6 done)

	Pruned	Kept	Total
New	860	9	869
Fresh	3	5	8
Picked	1	4	5
Done	0	2	2
Total	864	20	884

Accuracy

100.0%

Counts

884 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
▶	98.6%	(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
✓	98.6%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
	98.6%	(fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)
	98.6%	(fma.f64 (.f64 eps x) (fma.f64 x #s(literal -1/2 binary64) (.f64 (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) eps)) eps)
	98.6%	(fma.f64 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) eps)
	52.7%	(.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps))
▶	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))
	99.8%	(.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))
	36.2%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	98.8%	(.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)))
▶	98.8%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	98.5%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	99.4%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
	98.8%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	99.5%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
	5.8%	(.f64 eps (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
✓	99.6%	(*.f64 eps (cos.f64 x))
▶	97.9%	eps

Compiler

Compiled 546 to 322 computations (41% saved)

simplify651.0ms (4.5%)

Memory

-4.0MiB live, 746.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	cost-diff	640	(fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	cost-diff	320	(fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 eps x)
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
✓	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	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	320	(.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))

Rules

31 120×	`lower-fma.f32`
31 100×	`lower-fma.f64`
6 106×	`lower-+.f32`
6 104×	`lower-+.f64`
3 510×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	277
0	69	277
1	166	277
2	439	277
3	1122	270
4	2911	270
5	5097	270
6	5164	270
7	5179	270
8	5179	270
9	6992	270
10	7138	270
11	7151	270
12	7151	270
0	9423	253

Stop Event

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

Calls

Call 1

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

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

localize148.0ms (1%)

Memory

27.6MiB live, 254.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(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))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/12 binary64))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/12 binary64))
✓	accuracy	100.0%	(+.f64 eps x)
✓	accuracy	100.0%	(.f64 x (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
✓	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))

Samples

90.0ms

256×

valid

Compiler

Compiled 316 to 46 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 35.0ms (51.6% of total)

const: 15.0ms (22.1% of total)

ival-add: 14.0ms (20.6% of total)

ival-cos: 2.0ms (2.9% of total)

exact: 1.0ms (1.5% of total)

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

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

series26.0ms (0.2%)

Memory

13.5MiB live, 50.6MiB allocated

Counts

19 → 360

Calls

Call 1

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

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -1/24 (* (pow eps 3) (cos (* 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)>
#<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)) (* 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 eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps 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 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 (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)))))>
#<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 (* 1/12 (* eps (pow x 3)))>
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<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))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<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))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 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 (* 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 (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* 1/12 (pow x 3))>
#<alt (* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/12 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))>
#<alt -1/2>
#<alt (- (* 1/12 (pow x 2)) 1/2)>
#<alt (- (* 1/12 (pow x 2)) 1/2)>
#<alt (- (* 1/12 (pow x 2)) 1/2)>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* eps (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* eps (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* eps (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)))))>
#<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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (+ (* 1/12 (/ eps (pow x 3))) (* 1/24 (/ 1 (pow x 2)))) 1/720))>
#<alt (* (pow x 6) (- (+ (* 1/12 (/ eps (pow x 3))) (* 1/24 (/ 1 (pow x 2)))) (+ 1/720 (* 1/2 (/ 1 (pow x 4))))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (+ (* 1/12 (/ eps (pow x 3))) (* 1/24 (/ 1 (pow x 2)))) 1/720))>
#<alt (* (pow x 6) (- (+ (* -1 (/ (+ (* -1/12 eps) (* 1/2 (/ 1 x))) (pow x 3))) (* 1/24 (/ 1 (pow x 2)))) 1/720))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ 1 (+ (* eps (* x (- (* 1/12 (pow x 2)) 1/2))) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) 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 (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (* 1/12 (/ (pow eps 2) (pow x 3))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (* 1/12 (/ (pow eps 2) (pow x 3)))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (* 1/12 (/ (pow eps 2) (pow x 3))))))>
#<alt (* (pow x 6) (+ (* -1 (/ (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x))) (pow x 3))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt 1/24>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>

Calls

90 calls:

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

rewrite423.0ms (2.9%)

Memory

-5.5MiB live, 628.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 224×	`lower-fma.f32`
6 204×	`lower-fma.f64`
4 646×	`lower-*.f32`
4 620×	`lower-*.f64`
3 406×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	201
0	69	201
1	292	201
2	2354	201
0	8534	201

Stop Event

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

Counts

19 → 502

Calls

Call 1

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

Outputs
(.f64 eps (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(.f64 eps (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))
(.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.f64 #s(literal 2 binary64) (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) eps) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.f64 (.f64 #s(literal 2 binary64) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 (.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 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 eps #s(literal 1/2 binary64))))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (-.f64 (.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) (.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))))))
(.f64 eps (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) eps)
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) eps) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) (.f64 x (.f64 (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64))) (neg.f64 (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 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (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 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64))) (-.f64 (.f64 (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 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64))) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) #s(literal 3 binary64)) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))

simplify378.0ms (2.6%)

Memory

-19.6MiB live, 544.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 830×	`lower-fma.f64`
9 830×	`lower-fma.f32`
7 860×	`lower-*.f64`
7 860×	`lower-*.f32`
1 990×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	441	4676
1	1429	4481
2	4907	4459
0	8061	4055

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 348

Calls

Call 1

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

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -1/24 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal -1/24 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 eps eps))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
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(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal 1/6 binary64))))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/8 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(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))
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(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))
(* -1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(* -1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))

eval192.0ms (1.3%)

Memory: 12.5MiB live, 254.7MiB allocated
Compiler: Compiled 38 759 to 2 578 computations (93.3% saved)

prune133.0ms (0.9%)

Memory

14.6MiB live, 176.5MiB allocated

Pruning

22 alts after pruning (13 fresh and 9 done)

	Pruned	Kept	Total
New	933	7	940
Fresh	3	6	9
Picked	2	3	5
Done	0	6	6
Total	938	22	960

Accuracy

100.0%

Counts

960 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
✓	98.6%	(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
	98.8%	(fma.f64 (.f64 x x) (.f64 (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) eps)
✓	98.6%	(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
	98.6%	(fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)
	98.6%	(fma.f64 (.f64 eps x) (fma.f64 x #s(literal -1/2 binary64) (.f64 (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) eps)) eps)
	98.6%	(fma.f64 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) eps)
	52.7%	(.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps))
	99.9%	(.f64 (.f64 (/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) 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))
	99.9%	(.f64 (.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))) #s(literal 2 binary64))
	99.8%	(.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))
	98.8%	(.f64 eps (fma.f64 (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 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)))))
✓	98.8%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	99.4%	(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
	98.8%	(.f64 eps (fma.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	98.5%	(.f64 eps (fma.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	98.8%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	99.5%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
	5.1%	(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
✓	99.6%	(*.f64 eps (cos.f64 x))
✓	97.9%	eps

Compiler

Compiled 849 to 346 computations (59.2% saved)

regimes46.0ms (0.3%)

Memory

-21.8MiB live, 17.5MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 eps (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) 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 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) eps)
(fma.f64 (.f64 eps x) (fma.f64 x #s(literal -1/2 binary64) (.f64 (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.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 x x) (.f64 (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) eps)
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 (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 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
(.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps))
(.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 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (cos.f64 x)))
(.f64 (.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))) #s(literal 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 (/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) 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 (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 (.f64 eps eps) (sin.f64 x)) #s(literal -1/2 binary64) (*.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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

(*.f64 (*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) 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))

Calls

3 calls:

26.0ms	eps
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs
(.f64 (.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))) #s(literal 2 binary64))

Calls

3 calls:

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

regimes90.0ms (0.6%)

Memory

-18.1MiB live, 20.4MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs
(.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))

Calls

3 calls:

74.0ms	eps
7.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

25.0MiB live, 25.0MiB allocated

Counts

24 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.1%)

Memory

-17.1MiB live, 22.6MiB allocated

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

22.7MiB live, 22.7MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Memory

-14.1MiB live, 23.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

26.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps
5.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-12.6MiB live, 26.1MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs
(fma.f64 (.f64 x x) (.f64 (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) eps)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
eps
(*.f64 eps #s(literal 1 binary64))
(.f64 eps (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64)) eps)
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 eps x) eps)
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) 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 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) eps)
(fma.f64 (.f64 eps x) (fma.f64 x #s(literal -1/2 binary64) (.f64 (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(.f64 eps (fma.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/12 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.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	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

-17.7MiB live, 21.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.6%	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)

regimes9.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes8.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.6%	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)

regimes23.0ms (0.2%)

Memory

-31.2MiB live, 11.1MiB allocated

Accuracy

Total -59.4b remaining (-4376.6%)

Threshold costs -59.4b (-4376.6%)

Counts

4 → 1

Calls

Call 1

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

Outputs
eps

Calls

3 calls:

18.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Rules

54×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	210
1	99	210

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) 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 #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #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 (cos.f64 x))
(.f64 eps (fma.f64 (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 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)))))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (.f64 (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) 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 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
eps

Outputs
(.f64 (.f64 (/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) eps) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 (.f64 eps (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(.f64 #s(literal 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 (.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 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 eps #s(literal 1/2 binary64))))
(*.f64 eps (cos.f64 x))
(.f64 eps (fma.f64 (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 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)))))
(.f64 eps (fma.f64 (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 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))))
(.f64 eps (fma.f64 eps (.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (.f64 (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) 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)
(.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 x x) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps)
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
(fma.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) x)) eps)
eps

soundness1.6s (11.3%)

Memory

-12.4MiB live, 1 148.2MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
16 260×	`lower-fma.f64`
16 260×	`lower-fma.f32`
14 208×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	124
0	50	122
1	181	122
2	1341	122
0	8369	122
0	291	2090
1	893	1980
2	2341	1938
3	4842	1930
0	8433	1761
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	35	201
0	69	201
1	292	201
2	2354	201
0	8534	201
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	236	2923
1	773	2873
2	2453	2799
3	5300	2747
0	8330	2563
0	441	4676
1	1429	4481
2	4907	4459
0	8061	4055

Stop Event

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

Compiler

Compiled 626 to 323 computations (48.4% saved)

preprocess102.0ms (0.7%)

Memory: 34.0MiB live, 266.4MiB allocated
Compiler: Compiled 536 to 212 computations (60.4% 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%)

sample6.5s (45.3%)

preprocess25.0ms (0.2%)

explain147.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize80.0ms (0.6%)

series4.0ms (0%)

rewrite361.0ms (2.5%)

simplify361.0ms (2.5%)

eval36.0ms (0.2%)

prune31.0ms (0.2%)

simplify534.0ms (3.7%)

localize63.0ms (0.4%)

series19.0ms (0.1%)

rewrite343.0ms (2.4%)

simplify389.0ms (2.7%)

eval101.0ms (0.7%)

prune101.0ms (0.7%)

simplify51.0ms (0.4%)

localize96.0ms (0.7%)

series28.0ms (0.2%)

rewrite421.0ms (2.9%)

simplify361.0ms (2.5%)

eval122.0ms (0.8%)

prune142.0ms (1%)

simplify651.0ms (4.5%)

localize148.0ms (1%)

series26.0ms (0.2%)

rewrite423.0ms (2.9%)

simplify378.0ms (2.6%)

eval192.0ms (1.3%)

prune133.0ms (0.9%)

regimes46.0ms (0.3%)

regimes24.0ms (0.2%)

regimes90.0ms (0.6%)

regimes21.0ms (0.1%)

regimes21.0ms (0.1%)

regimes17.0ms (0.1%)

regimes38.0ms (0.3%)

regimes17.0ms (0.1%)

regimes14.0ms (0.1%)

regimes27.0ms (0.2%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes23.0ms (0.2%)

simplify8.0ms (0.1%)

soundness1.6s (11.3%)

preprocess102.0ms (0.7%)

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